General Relativity and Gravitation, ISSN 0001-7701, 6/2016, Volume 48, Issue 6, pp. 1 - 14

In this paper, under natural geometric and physical assumptions we provide new uniqueness and non-existence results for complete maximal hypersurfaces in...

53C42 | Lorentzian geometry | 53C50 | Maximal hypersurfaces | Theoretical, Mathematical and Computational Physics | Quantum Physics | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | Physics | Robertson–Walker spacetimes | 53C80 | Astronomy, Astrophysics and Cosmology | CONSTANT MEAN-CURVATURE | PHYSICS, MULTIDISCIPLINARY | SPACELIKE HYPERSURFACES | ASTRONOMY & ASTROPHYSICS | Robertson-Walker spacetimes | PHYSICS, PARTICLES & FIELDS

53C42 | Lorentzian geometry | 53C50 | Maximal hypersurfaces | Theoretical, Mathematical and Computational Physics | Quantum Physics | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | Physics | Robertson–Walker spacetimes | 53C80 | Astronomy, Astrophysics and Cosmology | CONSTANT MEAN-CURVATURE | PHYSICS, MULTIDISCIPLINARY | SPACELIKE HYPERSURFACES | ASTRONOMY & ASTROPHYSICS | Robertson-Walker spacetimes | PHYSICS, PARTICLES & FIELDS

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 01/2019, Volume 36, Issue 1, p. 15017

Several uniqueness results on compact maximal hypersurfaces in a wide class of globally hyperbolic spacetimes are provided. They are obtained from the study of...

globally hyperbolic spacetime | maximal hypersurface | compact spacelike hypersurface | EXISTENCE | CONSTANT MEAN-CURVATURE | PHYSICS, MULTIDISCIPLINARY | GENERALIZED ROBERTSON-WALKER | COMPLETE SPACELIKE HYPERSURFACES | UNIQUENESS | PRODUCTS | ASTRONOMY & ASTROPHYSICS | SURFACES | PHYSICS, PARTICLES & FIELDS

globally hyperbolic spacetime | maximal hypersurface | compact spacelike hypersurface | EXISTENCE | CONSTANT MEAN-CURVATURE | PHYSICS, MULTIDISCIPLINARY | GENERALIZED ROBERTSON-WALKER | COMPLETE SPACELIKE HYPERSURFACES | UNIQUENESS | PRODUCTS | ASTRONOMY & ASTROPHYSICS | SURFACES | PHYSICS, PARTICLES & FIELDS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 02/2019, Volume 179, pp. 354 - 382

We study the geometry of stable maximal hypersurfaces in a variety of spacetimes satisfying various physically relevant curvature assumptions, for instance the...

Spacetime of constant sectional curvature | [formula omitted]-stability | Stable maximal hypersurface | Generalized Robertson–Walker spacetime | k-stability | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | SUBMANIFOLDS | Generalized Robertson-Walker spacetime | SPACELIKE HYPERSURFACES | Stable maximal hypersurface k-stability | SURFACES | UNIQUENESS | Geometry | Hyperspaces | Stability | Curvature | Spacetime | Convergence | Mathematics - Differential Geometry

Spacetime of constant sectional curvature | [formula omitted]-stability | Stable maximal hypersurface | Generalized Robertson–Walker spacetime | k-stability | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | SUBMANIFOLDS | Generalized Robertson-Walker spacetime | SPACELIKE HYPERSURFACES | Stable maximal hypersurface k-stability | SURFACES | UNIQUENESS | Geometry | Hyperspaces | Stability | Curvature | Spacetime | Convergence | Mathematics - Differential Geometry

Journal Article

General Relativity and Gravitation, ISSN 0001-7701, 1/2019, Volume 51, Issue 1, pp. 1 - 66

In this work we study spacelike hypersurfaces immersed in spatially open standard static spacetimes with complete spacelike slices. Under appropriate lower...

53C42 | Calabi–Bernstein type result | 53C50 | Theoretical, Mathematical and Computational Physics | Geometric estimates | 58J05 | Quantum Physics | Physics | Astronomy, Astrophysics and Cosmology | Standard static spacetime | Complete spacelike hypersurface | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | PHYSICS, MULTIDISCIPLINARY | PROOF | Calabi-Bernstein type result | UNIQUENESS | GRAPHS | ASTRONOMY & ASTROPHYSICS | MEAN-CURVATURE | GEOMETRY | PHYSICS, PARTICLES & FIELDS | Mathematics - Differential Geometry

53C42 | Calabi–Bernstein type result | 53C50 | Theoretical, Mathematical and Computational Physics | Geometric estimates | 58J05 | Quantum Physics | Physics | Astronomy, Astrophysics and Cosmology | Standard static spacetime | Complete spacelike hypersurface | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | PHYSICS, MULTIDISCIPLINARY | PROOF | Calabi-Bernstein type result | UNIQUENESS | GRAPHS | ASTRONOMY & ASTROPHYSICS | MEAN-CURVATURE | GEOMETRY | PHYSICS, PARTICLES & FIELDS | Mathematics - Differential Geometry

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 06/2013, Volume 30, Issue 11, pp. 115007 - 13

A new technique for the study of noncompact complete spacelike hypersurfaces in generalized Robertson-Walker (GRW) spacetimes whose fiber is a parabolic...

CONSTANT MEAN-CURVATURE | PHYSICS, MULTIDISCIPLINARY | SPACELIKE HYPERSURFACES | ASTRONOMY & ASTROPHYSICS | HARMONIC-FUNCTIONS | ROUGH ISOMETRIES | RIEMANNIAN-MANIFOLDS | RELATIVITY | PHYSICS, PARTICLES & FIELDS | Geometry | Uniqueness | Cosmology | Fields (mathematics) | Compatibility | Manifolds (mathematics) | Quantum gravity | Fibers

CONSTANT MEAN-CURVATURE | PHYSICS, MULTIDISCIPLINARY | SPACELIKE HYPERSURFACES | ASTRONOMY & ASTROPHYSICS | HARMONIC-FUNCTIONS | ROUGH ISOMETRIES | RIEMANNIAN-MANIFOLDS | RELATIVITY | PHYSICS, PARTICLES & FIELDS | Geometry | Uniqueness | Cosmology | Fields (mathematics) | Compatibility | Manifolds (mathematics) | Quantum gravity | Fibers

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 4/2019, Volume 16, Issue 2, pp. 1 - 15

Complete spacelike hypersurfaces in spatially parabolic standard static spacetimes are studied. Under natural boundedness assumptions, we show how the...

Spacelike hypersurface | 53C42 | 53C50 | standard static spacetime | Mathematics, general | Calabi–Bernstein problem | 58J05 | Mathematics | parabolicity | 53C80 | Calabi-Bernstein problem | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | UNIQUENESS

Spacelike hypersurface | 53C42 | 53C50 | standard static spacetime | Mathematics, general | Calabi–Bernstein problem | 58J05 | Mathematics | parabolicity | 53C80 | Calabi-Bernstein problem | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | UNIQUENESS

Journal Article

General Relativity and Gravitation, ISSN 0001-7701, 10/2017, Volume 49, Issue 10, pp. 1 - 25

We provide some “half-space theorems” for spacelike complete non-compact hypersurfaces into orthogonally splitted spacetimes. In particular we generalize some...

CMC spacelike hypersurfaces | Parabolicity | Theoretical, Mathematical and Computational Physics | Orthogonally splitted spacetimes | Maximum principle | Quantum Physics | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | Physics | Astronomy, Astrophysics and Cosmology | CONSTANT MEAN-CURVATURE | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | UNIQUENESS | PHYSICS, PARTICLES & FIELDS

CMC spacelike hypersurfaces | Parabolicity | Theoretical, Mathematical and Computational Physics | Orthogonally splitted spacetimes | Maximum principle | Quantum Physics | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | Physics | Astronomy, Astrophysics and Cosmology | CONSTANT MEAN-CURVATURE | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | UNIQUENESS | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 08/2016, Volume 106, pp. 256 - 267

We study the geometry of null hypersurfaces M in generalized Robertson–Walker spacetimes. First we characterize such null hypersurfaces as graphs of...

Totally umbilical hypersurfaces | Parallel hypersurfaces | Totally geodesic | Null hypersurfaces | LIGHT-LIKE HYPERSURFACES | MATHEMATICS, APPLIED | SUBMANIFOLDS | SPACELIKE SURFACES | LORENTZ-MINKOWSKI SPACETIME | CONE | PHYSICS, MATHEMATICAL | GEOMETRY

Totally umbilical hypersurfaces | Parallel hypersurfaces | Totally geodesic | Null hypersurfaces | LIGHT-LIKE HYPERSURFACES | MATHEMATICS, APPLIED | SUBMANIFOLDS | SPACELIKE SURFACES | LORENTZ-MINKOWSKI SPACETIME | CONE | PHYSICS, MATHEMATICAL | GEOMETRY

Journal Article

Journal of Southeast University (English Edition), ISSN 1003-7985, 06/2018, Volume 34, Issue 2, pp. 276 - 280

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2015, Volume 367, Issue 9, pp. 6247 - 6266

any dimension, new examples of manifolds for which versions of the Positive Mass and Riemannian Penrose inequalities hold and discuss a notion of quasi-local...

YAMABE PROBLEM | MATHEMATICS | GENERAL-RELATIVITY | THEOREM | SPACELIKE HYPERSURFACES | PROOF | MANIFOLDS | SCALAR CURVATURE | ORDER MEAN-CURVATURE | DEFORMATION | RIEMANNIAN PENROSE INEQUALITY

YAMABE PROBLEM | MATHEMATICS | GENERAL-RELATIVITY | THEOREM | SPACELIKE HYPERSURFACES | PROOF | MANIFOLDS | SCALAR CURVATURE | ORDER MEAN-CURVATURE | DEFORMATION | RIEMANNIAN PENROSE INEQUALITY

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 12/2019, Volume 29, Issue 4, pp. 3293 - 3307

In this paper, we provide under certain geometric and physical assumptions new uniqueness and non-existence results for complete spacelike hypersurfaces of...

53C42 | 53C50 | Mathematics | Abstract Harmonic Analysis | Spacelike hypersurface | Fourier Analysis | Constant mean curvature | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | 53C80 | Generalized Robertson–Walker spacetime

53C42 | 53C50 | Mathematics | Abstract Harmonic Analysis | Spacelike hypersurface | Fourier Analysis | Constant mean curvature | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | 53C80 | Generalized Robertson–Walker spacetime

Journal Article

Manuscripta Mathematica, ISSN 0025-2611, 07/2017, Volume 153, Issue 3-4, pp. 431 - 454

We construct maximal hypersurfaces with a Neumann boundary condition in Minkowski space via mean curvature flow. In doing this we give general conditions for...

35K20 | 35K59 | 53C50 | 53C44 | MATHEMATICS | EVOLUTION | SPACELIKE HYPERSURFACES | MINKOWSKI SPACE | MEAN-CURVATURE FLOW | SURFACES | GRAPHS

35K20 | 35K59 | 53C50 | 53C44 | MATHEMATICS | EVOLUTION | SPACELIKE HYPERSURFACES | MINKOWSKI SPACE | MEAN-CURVATURE FLOW | SURFACES | GRAPHS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 09/2014, Volume 106, pp. 57 - 69

In this paper we provide several uniqueness and non-existence results for complete parabolic constant mean curvature spacelike hypersurfaces in Lorentzian...

Calabi–Bernstein problem | Parabolicity | Lorentzian warped products | Constant mean curvature spacelike hypersurfaces | Uniformly elliptic EDP’s | Calabi-Bernstein problem | Uniformly elliptic EDP's | MATHEMATICS, APPLIED | MINKOWSKI SPACE | MATHEMATICS | MAXIMAL SURFACES | HARMONIC-FUNCTIONS | ROBERTSON-WALKER SPACETIMES | RIEMANNIAN-MANIFOLDS | GEOMETRY | Nonlinearity | Constants | Mathematical analysis | Curvature | Uniqueness

Calabi–Bernstein problem | Parabolicity | Lorentzian warped products | Constant mean curvature spacelike hypersurfaces | Uniformly elliptic EDP’s | Calabi-Bernstein problem | Uniformly elliptic EDP's | MATHEMATICS, APPLIED | MINKOWSKI SPACE | MATHEMATICS | MAXIMAL SURFACES | HARMONIC-FUNCTIONS | ROBERTSON-WALKER SPACETIMES | RIEMANNIAN-MANIFOLDS | GEOMETRY | Nonlinearity | Constants | Mathematical analysis | Curvature | Uniqueness

Journal Article

Electronic Journal of Differential Equations, ISSN 1072-6691, 03/2018, Volume 2018, Issue 80, pp. 1 - 14

We apply some generalized maximum principles for establishing uniqueness and nonexistence results concerning maximal spacelike hypersurfaces immersed in a...

Maximal spacelike hypersurface equation | Entire graphs | Timelike convergence | Generalized Robertson-Walker spacetimes | Maximal spacelike hypersurfaces | MATHEMATICS | entire graphs | maximal spacelike hypersurface equation | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | SITTER SPACE | maximal spacelike hypersurfaces | timelike convergence | RIEMANNIAN-MANIFOLDS | UNIQUENESS | GEOMETRY

Maximal spacelike hypersurface equation | Entire graphs | Timelike convergence | Generalized Robertson-Walker spacetimes | Maximal spacelike hypersurfaces | MATHEMATICS | entire graphs | maximal spacelike hypersurface equation | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | SITTER SPACE | maximal spacelike hypersurfaces | timelike convergence | RIEMANNIAN-MANIFOLDS | UNIQUENESS | GEOMETRY

Journal Article

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Higher order mean curvature estimates for properly immersed ϕ h -bounded hypersurfaces

Annali di Matematica Pura ed Applicata, ISSN 0373-3114, 02/2019, Volume 198, Issue 1, pp. 157 - 175

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 01/2014, Volume 11, Issue 1, pp. 1450006 - 1-1450006-10

We provide upper and lower bounds for the volume of a compact spacelike hypersurface in an (n + 1)-dimensional Generalized Robertson-Walker (GRW) spacetime in...

Compact spacelike hypersurfaces | spatially closed Generalized Robertson-Walker spacetimes | PHYSICS, MATHEMATICAL | COSMOLOGICAL MODELS | Angles (geometry) | Lower bounds | Upper bounds | Eigenvalues | Warpage | Topology | Three dimensional | Fibers

Compact spacelike hypersurfaces | spatially closed Generalized Robertson-Walker spacetimes | PHYSICS, MATHEMATICAL | COSMOLOGICAL MODELS | Angles (geometry) | Lower bounds | Upper bounds | Eigenvalues | Warpage | Topology | Three dimensional | Fibers

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 12/2015, Volume 129, pp. 119 - 142

In this paper we deal with complete spacelike hypersurfaces in a generalized Robertson–Walker spacetime. Using as main analytical tool a new local form of the...

Generalized Robertson–Walker spacetimes | Weak maximum principle | Lorentzian mean curvature operator | Spacelike graphs | Generalized Robertson-Walker | spacetimes | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | Generalized Robertson-Walker spacetimes | UNIQUENESS | Geometry | Presses | Operators | Mathematical analysis | Maximum principle | Constants | Estimates | Curvature

Generalized Robertson–Walker spacetimes | Weak maximum principle | Lorentzian mean curvature operator | Spacelike graphs | Generalized Robertson-Walker | spacetimes | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | Generalized Robertson-Walker spacetimes | UNIQUENESS | Geometry | Presses | Operators | Mathematical analysis | Maximum principle | Constants | Estimates | Curvature

Journal Article

Asian Journal of Mathematics, ISSN 1093-6106, 2013, Volume 17, Issue 4, pp. 621 - 644

We consider the problem of whether a given spacetime admits a foliation by (n - 1)-umbilical spacelike hypersurfaces. We introduce the notion of a timelike...

(n - 1)-umbilical spacelike hypersurface | Closed partially conformal vector field | CONSTANT MEAN-CURVATURE | ROTATION HYPERSURFACES | MATHEMATICS, APPLIED | CONFORMAL VECTOR-FIELDS | GAP THEOREM | UNIQUENESS | MATHEMATICS | MULTIPLY WARPED PRODUCTS | LOCAL GEOMETRIC CHARACTERIZATION | SITTER SPACE | (n-1)-umbilical spacelike hypersurface | ROBERTSON-WALKER SPACETIMES | RIEMANNIAN-MANIFOLDS | 53A10 | (n−1)-umbilical spacelike hypersurfaces | 53C12

(n - 1)-umbilical spacelike hypersurface | Closed partially conformal vector field | CONSTANT MEAN-CURVATURE | ROTATION HYPERSURFACES | MATHEMATICS, APPLIED | CONFORMAL VECTOR-FIELDS | GAP THEOREM | UNIQUENESS | MATHEMATICS | MULTIPLY WARPED PRODUCTS | LOCAL GEOMETRIC CHARACTERIZATION | SITTER SPACE | (n-1)-umbilical spacelike hypersurface | ROBERTSON-WALKER SPACETIMES | RIEMANNIAN-MANIFOLDS | 53A10 | (n−1)-umbilical spacelike hypersurfaces | 53C12

Journal Article

Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, ISSN 1220-3874, 2017, Volume 60, Issue 1, pp. 33 - 49

In this paper, we apply several forms of generalized maximum principles to study the uniqueness of complete spacelike hypersurfaces immersed in Lorentzian...

Complete hyper- surface | Higher order mean curvature | Warping function | Lorentzian warped product | Spacelike slice | SPACETIMES | MATHEMATICS | spacelike slice | CONSTANT MEAN-CURVATURE | complete hyper surface | higher order mean curvature | RIGIDITY | MANIFOLDS | warping function | GEOMETRY | GRAPHS

Complete hyper- surface | Higher order mean curvature | Warping function | Lorentzian warped product | Spacelike slice | SPACETIMES | MATHEMATICS | spacelike slice | CONSTANT MEAN-CURVATURE | complete hyper surface | higher order mean curvature | RIGIDITY | MANIFOLDS | warping function | GEOMETRY | GRAPHS

Journal Article

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Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces

General Relativity and Gravitation, ISSN 0001-7701, 3/2015, Volume 47, Issue 3, pp. 1 - 20

We establish versions of the positive mass and Penrose inequalities for a class of asymptotically hyperbolic hypersurfaces. In particular, under the usual...

Theoretical, Mathematical and Computational Physics | 53C21 | 83C57 | Penrose inequality | 83C40 | Quantum Physics | Asymptotically hyperbolic hypersurfaces | Physics | Astronomy, Astrophysics and Cosmology | Cosmology | Positive mass conjecture | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | 53C80 | SPACETIMES | GENERAL-RELATIVITY | PHYSICS, MULTIDISCIPLINARY | THEOREM | PROOF | SCALAR CURVATURE RIGIDITY | FLOW | SPACELIKE HYPERSURFACES | ASTRONOMY & ASTROPHYSICS | MANIFOLDS | ORDER MEAN-CURVATURE | FORMULAS | PHYSICS, PARTICLES & FIELDS

Theoretical, Mathematical and Computational Physics | 53C21 | 83C57 | Penrose inequality | 83C40 | Quantum Physics | Asymptotically hyperbolic hypersurfaces | Physics | Astronomy, Astrophysics and Cosmology | Cosmology | Positive mass conjecture | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | 53C80 | SPACETIMES | GENERAL-RELATIVITY | PHYSICS, MULTIDISCIPLINARY | THEOREM | PROOF | SCALAR CURVATURE RIGIDITY | FLOW | SPACELIKE HYPERSURFACES | ASTRONOMY & ASTROPHYSICS | MANIFOLDS | ORDER MEAN-CURVATURE | FORMULAS | PHYSICS, PARTICLES & FIELDS

Journal Article

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