Mathematical Research Letters, ISSN 1073-2780, 2017, Volume 24, Issue 2, pp. 503 - 534

Let Sigma be an n(>= 3)-dimensional compact embedded hypersurface in a unit sphere with constant mean curvature H >= 0 and with two distinct principal...

constant mean curvature | Clifford hypersurface | INTEGRAL-INEQUALITIES | embedded hypersurface | MATHEMATICS | 2 PRINCIPAL CURVATURES | TORI | RIGIDITY | 3-SPHERE | S-3 | Simons-type identity | MINIMAL HYPERSURFACES | RIEMANNIAN-MANIFOLDS

constant mean curvature | Clifford hypersurface | INTEGRAL-INEQUALITIES | embedded hypersurface | MATHEMATICS | 2 PRINCIPAL CURVATURES | TORI | RIGIDITY | 3-SPHERE | S-3 | Simons-type identity | MINIMAL HYPERSURFACES | RIEMANNIAN-MANIFOLDS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2009, Volume 137, Issue 1, pp. 161 - 169

In this paper, using the Schauder fixed point theorem, we prove existence results of radial solutions for Dirichlet problems in the unit ball and in an annular...

Unit ball | Schauder fixed point theorem | Homeomorphism | Hypersurfaces | Minkowski space | Dirichlet problem | Boundary conditions | Mathematical constants | Euclidean space | Curvature | Radial solution | Mean curvature operator | PHI | MATHEMATICS | MATHEMATICS, APPLIED | radial solution | mean curvature operator

Unit ball | Schauder fixed point theorem | Homeomorphism | Hypersurfaces | Minkowski space | Dirichlet problem | Boundary conditions | Mathematical constants | Euclidean space | Curvature | Radial solution | Mean curvature operator | PHI | MATHEMATICS | MATHEMATICS, APPLIED | radial solution | mean curvature operator

Journal Article

2001, Lectures in mathematics ETH Zürich., ISBN 0817665765, 122

Book

Journal of Geometric Analysis, ISSN 1050-6926, 10/2017, Volume 27, Issue 4, pp. 3071 - 3084

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 2/2013, Volume 162, Issue 1, pp. 45 - 65

We describe all possible self-similar motions of immersed hypersurfaces in Euclidean space under the mean curvature flow and derive the corresponding...

Geometry | 53C42 | 53A10 | Constant mean curvature | 53C44 | Helicoidal surfaces | Mathematics | Mean curvature flow | MATHEMATICS | Mathematics - Differential Geometry

Geometry | 53C42 | 53A10 | Constant mean curvature | 53C44 | Helicoidal surfaces | Mathematics | Mean curvature flow | MATHEMATICS | Mathematics - Differential Geometry

Journal Article

Differential Geometry and its Applications, ISSN 0926-2245, 10/2017, Volume 54, pp. 264 - 281

In this paper we give a construction for discrete constant mean curvature surfaces in Riemannian spaceforms in terms of integrable systems techniques, which we...

Surface theory | Integrable systems | Discrete differential geometry | Singularities | Constant Gaussian curvature surfaces | ISOTHERMAL SURFACES | MATHEMATICS | MATHEMATICS, APPLIED | 3-SPACE | NETS | MAPS | FLAT SURFACES

Surface theory | Integrable systems | Discrete differential geometry | Singularities | Constant Gaussian curvature surfaces | ISOTHERMAL SURFACES | MATHEMATICS | MATHEMATICS, APPLIED | 3-SPACE | NETS | MAPS | FLAT SURFACES

Journal Article

Neural Computing and Applications, ISSN 0941-0643, 11/2016, Volume 27, Issue 8, pp. 2577 - 2586

In this paper, we present a method to generate a constant mean curvature (CMC) surface with the given boundary. By assuming the velocity to zero in the dynamic...

Computational Biology/Bioinformatics | Mesh optimizing | Variational model | Constant mean curvature | Computer Science | Data Mining and Knowledge Discovery | Image Processing and Computer Vision | Artificial Intelligence (incl. Robotics) | Surface tension | Computational Science and Engineering | Minimal surface | Probability and Statistics in Computer Science | APPROXIMATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Computational Biology/Bioinformatics | Mesh optimizing | Variational model | Constant mean curvature | Computer Science | Data Mining and Knowledge Discovery | Image Processing and Computer Vision | Artificial Intelligence (incl. Robotics) | Surface tension | Computational Science and Engineering | Minimal surface | Probability and Statistics in Computer Science | APPROXIMATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal Article

São Paulo Journal of Mathematical Sciences, ISSN 1982-6907, 6/2019, Volume 13, Issue 1, pp. 320 - 341

We derive sharp estimates for the infimum and supremum of the scalar curvature of a hypersurface immersed with constant mean curvature in a locally symmetric...

Constant mean curvature hypersurfaces | Primary 53C42 | Locally symmetric spaces | 53C50 | Mathematics, general | Mathematics | Secondary 53B30 | Scalar curvature estimates

Constant mean curvature hypersurfaces | Primary 53C42 | Locally symmetric spaces | 53C50 | Mathematics, general | Mathematics | Secondary 53B30 | Scalar curvature estimates

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2013, Volume 65, Issue 3, pp. 775 - 786

We prove the existence of a new class of constant mean curvature cylinders with an arbitrary number of umbilics by unitarizing the monodromy of Hill's equation.

Cylinder | Constant mean curvature | Hill's equation | MATHEMATICS | MONODROMY | MAPS | constant mean curvature | cylinder | SURFACES

Cylinder | Constant mean curvature | Hill's equation | MATHEMATICS | MONODROMY | MAPS | constant mean curvature | cylinder | SURFACES

Journal Article

Bulletin of the Brazilian Mathematical Society, New Series, ISSN 1678-7544, 9/2014, Volume 45, Issue 3, pp. 385 - 404

Let M n be a compact oriented hypersurface of a unit sphere $\mathbb{S}^{n + 1} $ (1) with constant mean curvature H. Given an integer k between 2 and n − 1,...

53C42 | 53A10 | hypersurfaces | Theoretical, Mathematical and Computational Physics | constant mean curvature | Mathematics, general | Mathematics | isoparametric hypersurfaces | product of spheres | MATHEMATICS | SPACE-FORMS | SCALAR CURVATURE | RIEMANNIAN-MANIFOLDS

53C42 | 53A10 | hypersurfaces | Theoretical, Mathematical and Computational Physics | constant mean curvature | Mathematics, general | Mathematics | isoparametric hypersurfaces | product of spheres | MATHEMATICS | SPACE-FORMS | SCALAR CURVATURE | RIEMANNIAN-MANIFOLDS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 363, Issue 2, pp. 579 - 587

In this paper we study the behavior of the scalar curvature S of a complete hypersurface immersed with constant mean curvature into a Riemannian space form of...

Ricci curvature | Scalar curvature | Maximum principle | Parabolicity | Stochastic completeness | Constant mean curvature | MATHEMATICS | MATHEMATICS, APPLIED | RIEMANNIAN-MANIFOLDS

Ricci curvature | Scalar curvature | Maximum principle | Parabolicity | Stochastic completeness | Constant mean curvature | MATHEMATICS | MATHEMATICS, APPLIED | RIEMANNIAN-MANIFOLDS

Journal Article

Annals of Global Analysis and Geometry, ISSN 0232-704X, 2015, Volume 47, Issue 3, pp. 225 - 238

We consider affine-complete Blaschke hypersurfaces with constant negative affine mean curvature; for a subclass we assume appropriate bounds for the affine...

Maximum principle of Omori–Yau | Negative affine mean curvature | Scalar curvature of the Blaschke metric | Affine spheres | MATHEMATICS | Maximum principle of Omori-Yau | Scalars | Constants | Operators | Theorems | Mathematical analysis | Curvature

Maximum principle of Omori–Yau | Negative affine mean curvature | Scalar curvature of the Blaschke metric | Affine spheres | MATHEMATICS | Maximum principle of Omori-Yau | Scalars | Constants | Operators | Theorems | Mathematical analysis | Curvature

Journal Article

The Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 1/2010, Volume 40, Issue 1, pp. 313 - 320

We obtain the explicit representation of Legendre surfaces in the unit 5-sphere with harmonic mean curvature vector field, under the condition that the mean...

Tangents | Mathematical theorems | Vector fields | Mathematical constants | Mathematical surfaces | Mathematical vectors | Mathematical functions | Curvature | Harmonic mean | MATHEMATICS | 53C42 | 53B25

Tangents | Mathematical theorems | Vector fields | Mathematical constants | Mathematical surfaces | Mathematical vectors | Mathematical functions | Curvature | Harmonic mean | MATHEMATICS | 53C42 | 53B25

Journal Article

74.
Full Text
Constant mean curvature hypersurfaces with constant angle in semi-Riemannian space forms

Differential Geometry and its Applications, ISSN 0926-2245, 12/2016, Volume 49, pp. 473 - 495

We study constant angle semi-Riemannian hypersurfaces M immersed in semi-Riemannian space forms, where the constant angle is defined in terms of a closed and...

Closed and conformal vector field | Constant mean curvature | Constant angle hypersurfaces | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCT | CLASSIFICATION | H-2 X R | 3-DIMENSIONAL MINKOWSKI SPACE | FOLIATED SPACETIMES | SURFACES

Closed and conformal vector field | Constant mean curvature | Constant angle hypersurfaces | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCT | CLASSIFICATION | H-2 X R | 3-DIMENSIONAL MINKOWSKI SPACE | FOLIATED SPACETIMES | SURFACES

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2014, Volume 142, Issue 9, pp. 3237 - 3248

We obtain a Calabi-Yau type volume growth estimate for complete noncompact self-shrinkers of the mean curvature flow. More precisely, every complete noncompact...

Integers | Geometry | Riemann manifold | Mathematical theorems | Mathematical growth | Solitons | Mathematical constants | Euclidean space | Mathematical inequalities | Curvature | Self-shrinker | Volume growth estimate | Mean curvature flow | MATHEMATICS | MATHEMATICS, APPLIED | SUBMANIFOLDS | LOGARITHMIC SOBOLEV INEQUALITIES | volume growth estimate | mean curvature flow | RICCI SOLITONS

Integers | Geometry | Riemann manifold | Mathematical theorems | Mathematical growth | Solitons | Mathematical constants | Euclidean space | Mathematical inequalities | Curvature | Self-shrinker | Volume growth estimate | Mean curvature flow | MATHEMATICS | MATHEMATICS, APPLIED | SUBMANIFOLDS | LOGARITHMIC SOBOLEV INEQUALITIES | volume growth estimate | mean curvature flow | RICCI SOLITONS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2014, Volume 366, Issue 7, pp. 3373 - 3388

This paper demonstrates existence for all time of mean curvature flow in Minkowski space with a perpendicular Neumann boundary condition, where the boundary...

Mathematical manifolds | Neumann problem | Evolution equations | Hypersurfaces | Hyperplanes | Minkowski space | Boundary conditions | Mathematical constants | Convexity | Curvature | MATHEMATICS | SPACELIKE HYPERSURFACES | SURFACES

Mathematical manifolds | Neumann problem | Evolution equations | Hypersurfaces | Hyperplanes | Minkowski space | Boundary conditions | Mathematical constants | Convexity | Curvature | MATHEMATICS | SPACELIKE HYPERSURFACES | SURFACES

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 03/2014, Volume 31, Issue 5, p. 55001

A decomposition of linear gravitational perturbations in 1 + d form is presented which differs in several respects from earlier ones. (i) The boundary value...

gauge slices | Moncrief decomposition | gravitational perturbations | gauge invariant action | lapse-weighted transversal-traceless decomposition | ROBERTSON-WALKER MODELS | QUANTUM SCIENCE & TECHNOLOGY | SYMMETRIES | PHYSICS, MULTIDISCIPLINARY | GAUGE TRANSFORMATIONS | LINEARIZATION STABILITY | EINSTEIN EQUATION | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Mathematical analysis | Constants | Decomposition | Perturbation | Gages | Curvature | Quantum gravity | Gauges

gauge slices | Moncrief decomposition | gravitational perturbations | gauge invariant action | lapse-weighted transversal-traceless decomposition | ROBERTSON-WALKER MODELS | QUANTUM SCIENCE & TECHNOLOGY | SYMMETRIES | PHYSICS, MULTIDISCIPLINARY | GAUGE TRANSFORMATIONS | LINEARIZATION STABILITY | EINSTEIN EQUATION | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Mathematical analysis | Constants | Decomposition | Perturbation | Gages | Curvature | Quantum gravity | Gauges

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2009, Volume 137, Issue 2, pp. 711 - 721

We consider complete spacelike hypersurfaces with constant mean curvature in the open region of de Sitter space known as the steady state space. We prove that...

Riemann manifold | Tensors | Infinity | Spacetime | Hypersurfaces | Vector fields | Mathematical constants | Curvature | Simply connected regions | Spacelike hypersurface | Mean | De Sitter space | Steady state space | steady state space | MATHEMATICS | MATHEMATICS, APPLIED | mean curvature | parabolicity | de Sitter space | spacelike hypersurface

Riemann manifold | Tensors | Infinity | Spacetime | Hypersurfaces | Vector fields | Mathematical constants | Curvature | Simply connected regions | Spacelike hypersurface | Mean | De Sitter space | Steady state space | steady state space | MATHEMATICS | MATHEMATICS, APPLIED | mean curvature | parabolicity | de Sitter space | spacelike hypersurface

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 08/2016, Volume 106, pp. 352 - 366

Constant mean curvature (CMC) tori in Euclidean 3-space are described by an algebraic curve, called the spectral curve, together with a line bundle on this...

Spectral curves | Constant mean curvature tori | Integrable systems

Spectral curves | Constant mean curvature tori | Integrable systems

Journal Article

80.
Full Text
Steady State and Long Time Convergence of Spirals Moving by Forced Mean Curvature Motion

Communications in Partial Differential Equations, ISSN 0360-5302, 06/2015, Volume 40, Issue 6, pp. 1137 - 1181

In this paper, we prove the existence and uniqueness of a "steady" spiral moving with forced mean curvature motion. This spiral has a stationary shape and...

Spirals | Motion of interfaces | 35A05 | Liouville theorem | Mean curvature motion | 35D40 | Long time convergence | Steady state | 35K55 | Viscosity solutions | 35K65 | EXISTENCE | MATHEMATICS, APPLIED | HEAT-EQUATIONS | SINGULARITIES | BEHAVIOR | MODEL | UNIQUENESS | MATHEMATICS | EXCITABLE MEDIA | CRYSTAL-GROWTH | CURVE | BLOW-UP | Partial differential equations | Economic models | Convergence | Mathematical analysis | Constants | Angular velocity | Curvature | Cauchy problem | Analysis of PDEs | Mathematics

Spirals | Motion of interfaces | 35A05 | Liouville theorem | Mean curvature motion | 35D40 | Long time convergence | Steady state | 35K55 | Viscosity solutions | 35K65 | EXISTENCE | MATHEMATICS, APPLIED | HEAT-EQUATIONS | SINGULARITIES | BEHAVIOR | MODEL | UNIQUENESS | MATHEMATICS | EXCITABLE MEDIA | CRYSTAL-GROWTH | CURVE | BLOW-UP | Partial differential equations | Economic models | Convergence | Mathematical analysis | Constants | Angular velocity | Curvature | Cauchy problem | Analysis of PDEs | Mathematics

Journal Article

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