Science China Mathematics, ISSN 1674-7283, 1/2019, Volume 62, Issue 1, pp. 157 - 170

In this article, we study the short-time existence of conformal Ricci flow on asymptotically hyperbolic manifolds...

conformal Ricci flow | asymptotically hyperbolic manifolds | local Shi’s curvature derivative estimates | short time existence | 58J05 | Mathematics | Applications of Mathematics | 53C25 | local Shi's curvature derivative estimates | MATHEMATICS | MATHEMATICS, APPLIED | METRICS

conformal Ricci flow | asymptotically hyperbolic manifolds | local Shi’s curvature derivative estimates | short time existence | 58J05 | Mathematics | Applications of Mathematics | 53C25 | local Shi's curvature derivative estimates | MATHEMATICS | MATHEMATICS, APPLIED | METRICS

Journal Article

Classical and quantum gravity, ISSN 1361-6382, 2018, Volume 35, Issue 11, p. 115015

We prove positivity of energy for a class of asymptotically locally hyperbolic manifolds in dimensions 4 <= n <= 7...

metric deformation | hyperbolic mass | mass aspect | asymptotically hyperbolic manifolds | QUANTUM SCIENCE & TECHNOLOGY | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | RIGIDITY | PHYSICS, PARTICLES & FIELDS

metric deformation | hyperbolic mass | mass aspect | asymptotically hyperbolic manifolds | QUANTUM SCIENCE & TECHNOLOGY | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | RIGIDITY | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Spectral Theory, ISSN 1664-039X, 2016, Volume 6, Issue 4, pp. 1087 - 1114

... for (even) asymptotically hyperbolic manifolds. It provides an effective definition of resonances in that setting by identifying them with poles of inverses of a family of Fredholm differential operators...

Asymptotically hyperbolic manifolds | Scattering resonances | SPECTRAL THEORY | MATHEMATICS, APPLIED | NON-EUCLIDEAN SPACES | RIEMANN SURFACE | EISENSTEIN SERIES | BLACK-HOLES | MATHEMATICS | MICROLOCAL ANALYSIS | scattering resonances | RESOLVENT | LAPLACIAN OPERATOR | CONSTANT NEGATIVE CURVATURE | KERR-DE SITTER

Asymptotically hyperbolic manifolds | Scattering resonances | SPECTRAL THEORY | MATHEMATICS, APPLIED | NON-EUCLIDEAN SPACES | RIEMANN SURFACE | EISENSTEIN SERIES | BLACK-HOLES | MATHEMATICS | MICROLOCAL ANALYSIS | scattering resonances | RESOLVENT | LAPLACIAN OPERATOR | CONSTANT NEGATIVE CURVATURE | KERR-DE SITTER

Journal Article

Journal of Spectral Theory, ISSN 1664-039X, 2019, Volume 9, Issue 1, pp. 269 - 313

We obtain a formula for the Schwartz kernel of the scattering operator in terms of the Schwartz kernel of the forward fundamental solution of the wave operator on asymptotically hyperbolic manifolds...

Wave equation | Scattering relation | Asymptotically hyperbolic manifolds | Scattering | Radiation fields | FIELDS | MATHEMATICS, APPLIED | X-RAY TRANSFORM | INVERSE SCATTERING | scattering relation | wave equation | LAPLACE OPERATOR | MATHEMATICS | scattering | RESOLVENT | RIGIDITY | radiation fields | CONTINUATION

Wave equation | Scattering relation | Asymptotically hyperbolic manifolds | Scattering | Radiation fields | FIELDS | MATHEMATICS, APPLIED | X-RAY TRANSFORM | INVERSE SCATTERING | scattering relation | wave equation | LAPLACE OPERATOR | MATHEMATICS | scattering | RESOLVENT | RIGIDITY | radiation fields | CONTINUATION

Journal Article

Advances in Mathematics, ISSN 0001-8708, 07/2012, Volume 230, Issue 4-6, pp. 2332 - 2363

.... As a consequence we prove some rigidity theorems for complete manifolds whose curvature tends to the hyperbolic one in a rate greater than 2.

Rigidity | Regularity up to the boundary | Asymptotically hyperbolic | Conformally compact manifold | MATHEMATICS | CURVATURE RIGIDITY

Rigidity | Regularity up to the boundary | Asymptotically hyperbolic | Conformally compact manifold | MATHEMATICS | CURVATURE RIGIDITY

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 03/2014, Volume 25, Issue 3, pp. 1450020 - 1-1450020-25

Let (M, g) be an Asymptotically Locally Hyperbolic (ALH) manifold which is the interior of a conformally compact manifold and (∂M, [γ...

Twistor spinors | Killing spinors | Dirac operator | Asymptotically hyperbolic manifold | Conformally compact manifold | Einstein manifold | MATHEMATICS | CONFORMAL DEFORMATION | asymptotically hyperbolic manifold | MASS | CURVATURE | Manifolds | Infinity | Asymptotic properties | Mathematical analysis | Scalars | Rigidity | Boundaries | Curvature | Supersymmetry | Mathematics | Differential Geometry | Mathematical Physics | General Mathematics

Twistor spinors | Killing spinors | Dirac operator | Asymptotically hyperbolic manifold | Conformally compact manifold | Einstein manifold | MATHEMATICS | CONFORMAL DEFORMATION | asymptotically hyperbolic manifold | MASS | CURVATURE | Manifolds | Infinity | Asymptotic properties | Mathematical analysis | Scalars | Rigidity | Boundaries | Curvature | Supersymmetry | Mathematics | Differential Geometry | Mathematical Physics | General Mathematics

Journal Article

Communications in partial differential equations, ISSN 1532-4133, 2016, Volume 41, Issue 3, pp. 515 - 578

This is the first in a series of papers in which we investigate the resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds with applications to the restriction theorem...

fourier integral operator | Asymptotically hyperbolic manifolds | resolvent | semiclassical analysis | intersecting Lagrangian distribution | MATHEMATICS, APPLIED | SPACES | 58J40 | 58J50 | MATHEMATICS | SEMICLASSICAL RESOLVENT | CONTINUATION | PROPAGATOR | Manifolds | Construction | Energy use | Multipliers | Partial differential equations | Asymptotic properties | Spectra | Estimates

fourier integral operator | Asymptotically hyperbolic manifolds | resolvent | semiclassical analysis | intersecting Lagrangian distribution | MATHEMATICS, APPLIED | SPACES | 58J40 | 58J50 | MATHEMATICS | SEMICLASSICAL RESOLVENT | CONTINUATION | PROPAGATOR | Manifolds | Construction | Energy use | Multipliers | Partial differential equations | Asymptotic properties | Spectra | Estimates

Journal Article

Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 05/2018, Volume 35, Issue 3, pp. 803 - 829

In the present paper, we investigate global-in-time Strichartz estimates without loss on non-trapping asymptotically hyperbolic manifolds...

Spectral measure | Strichartz estimates | Asymptotically hyperbolic manifolds | Dispersive estimates | WAVE | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | INEQUALITIES | SPACES | CONTINUATION | SURFACES

Spectral measure | Strichartz estimates | Asymptotically hyperbolic manifolds | Dispersive estimates | WAVE | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | INEQUALITIES | SPACES | CONTINUATION | SURFACES

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2013, Volume 141, Issue 1, pp. 313 - 324

In this paper, we will show that the limit of some quasilocal mass integrals of the coordinate spheres in an asymptotically hyperbolic (AH...

Asymptotically hyperbolic manifolds | Quasilocal mass integral | Isometric embedding | MATHEMATICS | MATHEMATICS, APPLIED | isometric embedding | asymptotically hyperbolic manifolds | THEOREM | RIGIDITY | BOUNDARY | SCALAR CURVATURE | COMPACT MANIFOLDS

Asymptotically hyperbolic manifolds | Quasilocal mass integral | Isometric embedding | MATHEMATICS | MATHEMATICS, APPLIED | isometric embedding | asymptotically hyperbolic manifolds | THEOREM | RIGIDITY | BOUNDARY | SCALAR CURVATURE | COMPACT MANIFOLDS

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 3/2012, Volume 310, Issue 3, pp. 705 - 763

We construct solutions of the constraint equation with non constant mean curvature on an asymptotically hyperbolic manifold by the conformal method...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | PHYSICS, MATHEMATICAL | General Relativity and Quantum Cosmology | Mathematics | Differential Geometry | Analysis of PDEs

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | PHYSICS, MATHEMATICAL | General Relativity and Quantum Cosmology | Mathematics | Differential Geometry | Analysis of PDEs

Journal Article

Annales de l'Institut Fourier, ISSN 0373-0956, 2018, Volume 68, Issue 3, pp. 1011 - 1075

We consider the Laplacian Delta on an asymptotically hyperbolic manifold X, as defined by Mazzeo and Melrose...

Restriction theorem | Spectral measure | Asymptotically hyperbolic manifolds | Spectral multiplier | MATHEMATICS | WAVE | spectral multiplier | restriction theorem | SPACES | SCATTERING | CONTINUATION | spectral measure | SCHRODINGER-OPERATORS

Restriction theorem | Spectral measure | Asymptotically hyperbolic manifolds | Spectral multiplier | MATHEMATICS | WAVE | spectral multiplier | restriction theorem | SPACES | SCATTERING | CONTINUATION | spectral measure | SCHRODINGER-OPERATORS

Journal Article

Analysis and PDE, ISSN 2157-5045, 2015, Volume 8, Issue 3, pp. 513 - 559

We prove a local support theorem for the radiation fields on asymptotically hyperbolic manifolds and use it to show that the scattering operator restricted to an open subset of the boundary...

Inverse scattering | Asymptotically hyperbolic manifolds | MATHEMATICS | MATHEMATICS, APPLIED | RADIATION-FIELDS | asymptotically hyperbolic manifolds | THEOREM | inverse scattering | WAVE-EQUATION | ABSENCE | OPERATORS | UNIQUE CONTINUATION | RIEMANNIAN-MANIFOLDS | Mathematics - Analysis of PDEs

Inverse scattering | Asymptotically hyperbolic manifolds | MATHEMATICS | MATHEMATICS, APPLIED | RADIATION-FIELDS | asymptotically hyperbolic manifolds | THEOREM | inverse scattering | WAVE-EQUATION | ABSENCE | OPERATORS | UNIQUE CONTINUATION | RIEMANNIAN-MANIFOLDS | Mathematics - Analysis of PDEs

Journal Article

Analysis and PDE, ISSN 2157-5045, 2011, Volume 4, Issue 1, pp. 1 - 84

Journal Article

Asymptotic Analysis, ISSN 0921-7134, 2014, Volume 90, Issue 3-4, pp. 281 - 323

We study the spectral theory of asymptotically hyperbolic manifolds with ends of warped-product type...

asymptotically hyperbolic | spectral theory | resonances | SHARP UPPER-BOUNDS | MATHEMATICS, APPLIED | NUMBER | SCATTERING POLES | COMPLETE SPACES | RESOLVENT | CONSTANT NEGATIVE CURVATURE

asymptotically hyperbolic | spectral theory | resonances | SHARP UPPER-BOUNDS | MATHEMATICS, APPLIED | NUMBER | SCATTERING POLES | COMPLETE SPACES | RESOLVENT | CONSTANT NEGATIVE CURVATURE

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 10/2009, Volume 242, Issue 2, pp. 377 - 397

We prove a dynamical wave trace formula for asymptotically hyperbolic (n + 1)-dimensional manifolds with negative...

Prime orbit theorem | Geodesic length spectrum | Dynamics | Topological entropy | Asymptotically hyperbolic | Negative curvature | Trace formula | Regularized wave trace | Geodesic flow | topological entropy | PRIME NUMBER THEOREM | prime orbit theorem | trace formula | asymptotically hyperbolic | negative curvature | geodesic flow | LENGTH SPECTRUM | MATHEMATICS | geodesic length spectrum | dynamics | regularized wave trace | GEODESIC-FLOWS | LOWER BOUNDS | NEGATIVELY CURVED MANIFOLDS | SELBERGS ZETA-FUNCTION | CONJUGATE-POINTS | RESONANCES | RIEMANNIAN-MANIFOLDS | Matematik | Mathematics

Prime orbit theorem | Geodesic length spectrum | Dynamics | Topological entropy | Asymptotically hyperbolic | Negative curvature | Trace formula | Regularized wave trace | Geodesic flow | topological entropy | PRIME NUMBER THEOREM | prime orbit theorem | trace formula | asymptotically hyperbolic | negative curvature | geodesic flow | LENGTH SPECTRUM | MATHEMATICS | geodesic length spectrum | dynamics | regularized wave trace | GEODESIC-FLOWS | LOWER BOUNDS | NEGATIVELY CURVED MANIFOLDS | SELBERGS ZETA-FUNCTION | CONJUGATE-POINTS | RESONANCES | RIEMANNIAN-MANIFOLDS | Matematik | Mathematics

Journal Article

Journal of geometry and physics, ISSN 0393-0440, 2018, Volume 132, pp. 338 - 357

.... There is a natural analogue of the Bartnik mass for asymptotically hyperbolic Riemannian manifolds with a negative lower bound on scalar curvature which model time-symmetric domains obeying...

Bounded scalar curvature | Asymptotically hyperbolic manifolds | Quasi-local mass | MATHEMATICS | THEOREM | CURVATURE | MANIFOLDS | PHYSICS, MATHEMATICAL | FLOW

Bounded scalar curvature | Asymptotically hyperbolic manifolds | Quasi-local mass | MATHEMATICS | THEOREM | CURVATURE | MANIFOLDS | PHYSICS, MATHEMATICAL | FLOW

Journal Article

Annals of global analysis and geometry, ISSN 1572-9060, 2019, Volume 56, Issue 3, pp. 443 - 463

The positive mass theorem states that the total mass of a complete asymptotically flat manifold with nonnegative scalar curvature is nonnegative...

Geometry | Mathematical Physics | Analysis | Global Analysis and Analysis on Manifolds | Mathematics | Differential Geometry | Stability of hyperbolic positive mass theorem | Asymptotically hyperbolic manifolds | Asymptotically hyperbolic graphs | MATHEMATICS | PENROSE INEQUALITY | NEAR-EQUALITY | FLAT | PROOF | Employee motivation | Theorems | Euclidean geometry | Asymptotic properties | Graphs | Euclidean space | Dimensional stability | Manifolds (mathematics) | Curvature

Geometry | Mathematical Physics | Analysis | Global Analysis and Analysis on Manifolds | Mathematics | Differential Geometry | Stability of hyperbolic positive mass theorem | Asymptotically hyperbolic manifolds | Asymptotically hyperbolic graphs | MATHEMATICS | PENROSE INEQUALITY | NEAR-EQUALITY | FLAT | PROOF | Employee motivation | Theorems | Euclidean geometry | Asymptotic properties | Graphs | Euclidean space | Dimensional stability | Manifolds (mathematics) | Curvature

Journal Article

Communications in partial differential equations, ISSN 0360-5302, 04/2020, pp. 1 - 41

...1. IntroductionThe heat kernel on a manifold M is the positive fundamental solution of the following Cauchy problem in (1.1) where and ΔM is the positive...

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 01/2016, Volume 69, Issue 1, pp. 124 - 144

We prove a sharp inequality for hypersurfaces in the n‐dimensional anti‐de Sitter‐Schwarzschild manifold for general n...

SPACE | MATHEMATICS | MATHEMATICS, APPLIED | PENROSE INEQUALITY | MEAN-CURVATURE | ASYMPTOTICALLY HYPERBOLIC MANIFOLDS | SCALAR CURVATURE RIGIDITY | QUASI-LOCAL MASS | POSITIVITY | FLOW | RIEMANNIAN-MANIFOLDS | SURFACES

SPACE | MATHEMATICS | MATHEMATICS, APPLIED | PENROSE INEQUALITY | MEAN-CURVATURE | ASYMPTOTICALLY HYPERBOLIC MANIFOLDS | SCALAR CURVATURE RIGIDITY | QUASI-LOCAL MASS | POSITIVITY | FLOW | RIEMANNIAN-MANIFOLDS | SURFACES

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 06/2017, Volume 369, Issue 6, pp. 4385 - 4413

for conformally compact Einstein manifolds. This leads not only to the complete proof of the rigidity theorem for conformally compact Einstein manifolds...

Curvature estimates | Gap phenomena | Yamabe constants | Rigidity | Conformally compact einstein manifolds | Renormalized volumes | curvature estimates | Conformally compact Einstein manifolds | gap phenomena | METRICS | rigidity | INFINITY | MATHEMATICS | REGULARITY | MASS | ASYMPTOTICALLY HYPERBOLIC MANIFOLDS | renormalized volumes | 4-MANIFOLDS

Curvature estimates | Gap phenomena | Yamabe constants | Rigidity | Conformally compact einstein manifolds | Renormalized volumes | curvature estimates | Conformally compact Einstein manifolds | gap phenomena | METRICS | rigidity | INFINITY | MATHEMATICS | REGULARITY | MASS | ASYMPTOTICALLY HYPERBOLIC MANIFOLDS | renormalized volumes | 4-MANIFOLDS

Journal Article

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