Mathematische Zeitschrift, ISSN 0025-5874, 10/2019, Volume 293, Issue 1, pp. 485 - 502

... conformal compactification of some Poincare–Einstein metric must be the standard hemisphere when the first nonzero eigenvalue of the Dirac operator achieves its lowest value, and any $$C^{3,\alpha }$$ C 3 , α...

Poincare–Einstein metric | Eigenvalue | Yamabe invariant | Mathematics, general | Mathematics | Dirac operator | Boundary condition | MATHEMATICS | CONSTANT MEAN-CURVATURE | CONFORMAL DEFORMATION | BOUNDARY-VALUE-PROBLEMS | MANIFOLDS | SPECTRAL ASYMMETRY | Poincare-Einstein metric

Poincare–Einstein metric | Eigenvalue | Yamabe invariant | Mathematics, general | Mathematics | Dirac operator | Boundary condition | MATHEMATICS | CONSTANT MEAN-CURVATURE | CONFORMAL DEFORMATION | BOUNDARY-VALUE-PROBLEMS | MANIFOLDS | SPECTRAL ASYMMETRY | Poincare-Einstein metric

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2006, Volume 204, Issue 2, pp. 379 - 412

We establish a boundary connected sum theorem for asymptotically hyperbolic Einstein metrics, and also show that if the two metrics have scalar positive conformal infinities, then the same is true for this boundary join...

Gluing | Uniformly degenerate operators | Poincaré–Einstein | Poincaré-Einstein | INFINITY | MATHEMATICS | Poincare-Einstein | REGULARITY | VOLUME | gluing | POSITIVE SCALAR CURVATURE | MANIFOLDS | uniformly degenerate operators | 4-MANIFOLDS

Gluing | Uniformly degenerate operators | Poincaré–Einstein | Poincaré-Einstein | INFINITY | MATHEMATICS | Poincare-Einstein | REGULARITY | VOLUME | gluing | POSITIVE SCALAR CURVATURE | MANIFOLDS | uniformly degenerate operators | 4-MANIFOLDS

Journal Article

Analysis and PDE, ISSN 2157-5045, 2017, Volume 10, Issue 2, pp. 253 - 280

Under a spectral assumption on the Laplacian of a Poincare-Einstein manifold, we establish an energy inequality relating the energy of a fractional GJMS...

Smooth metric measure space | Fractional GJMS operator | Fractional Laplacian | Robin operator | Poincaré-Einstein manifold | Poincare-Einstein manifold | MATHEMATICS, APPLIED | fractional GJMS operator | SOBOLEV INEQUALITIES | LAPLACIAN | MATHEMATICS | CONFORMAL DEFORMATION | smooth metric measure space | EINSTEIN-METRICS | fractional Laplacian | BOUNDARY | MANIFOLDS | SHARP CONSTANTS | GEOMETRY

Smooth metric measure space | Fractional GJMS operator | Fractional Laplacian | Robin operator | Poincaré-Einstein manifold | Poincare-Einstein manifold | MATHEMATICS, APPLIED | fractional GJMS operator | SOBOLEV INEQUALITIES | LAPLACIAN | MATHEMATICS | CONFORMAL DEFORMATION | smooth metric measure space | EINSTEIN-METRICS | fractional Laplacian | BOUNDARY | MANIFOLDS | SHARP CONSTANTS | GEOMETRY

Journal Article

INDIANA UNIVERSITY MATHEMATICS JOURNAL, ISSN 0022-2518, 2018, Volume 67, Issue 1, pp. 293 - 327

We describe a set of conformally covariant boundary operators associated to the Paneitz operator, in the sense that they give rise to a conformally covariant...

MATHEMATICS | Poincare-Einstein manifold | CONSTANT MEAN-CURVATURE | boundary operator | Conformally covariant operator | DETERMINANTS | fractional Laplacian | MANIFOLDS | Sobolev trace inequality | SCALAR-FLAT METRICS | SOBOLEV

MATHEMATICS | Poincare-Einstein manifold | CONSTANT MEAN-CURVATURE | boundary operator | Conformally covariant operator | DETERMINANTS | fractional Laplacian | MANIFOLDS | Sobolev trace inequality | SCALAR-FLAT METRICS | SOBOLEV

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 1/2012, Volume 165, Issue 1, pp. 15 - 39

... with intersecting scale singularities and identify the scale singularity as minimal submanifold with respect to certain metrics in the underlying conformal class...

53C42 | Conformal geometry and tractor calculus | Conformal holonomy | Primary 53A30 | Mathematics, general | Mathematics | 53C25 | Almost Einstein structures and Poincaré–Einstein metrics | Strongly umbilic and minimal submanifolds | Secondary 53C29 | Almost Einstein structures and Poincaré-Einstein metrics | MATHEMATICS | Almost Einstein structures and Poincare-Einstein metrics | MANIFOLDS | SIGNATURE

53C42 | Conformal geometry and tractor calculus | Conformal holonomy | Primary 53A30 | Mathematics, general | Mathematics | 53C25 | Almost Einstein structures and Poincaré–Einstein metrics | Strongly umbilic and minimal submanifolds | Secondary 53C29 | Almost Einstein structures and Poincaré-Einstein metrics | MATHEMATICS | Almost Einstein structures and Poincare-Einstein metrics | MANIFOLDS | SIGNATURE

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 2014, Volume 163, Issue 5, pp. 1035 - 1070

We develop a holonomy reduction procedure for general Cartan geometries. We show that, given a reduction of holonomy, the underlying manifold naturally...

MATHEMATICS | SPACES | INVARIANTS | METRICS | EXCEPTIONAL HOLONOMY | CONFORMAL HOLONOMY | DIFFERENTIAL-EQUATIONS | CLASSIFICATION | PARABOLIC GEOMETRIES | POINCARE-EINSTEIN MANIFOLDS | CONNECTIONS | Mathematics - Differential Geometry | 53A20 | 53A30 | 58J70 | 32V05 | 53B15 | 58D19 | 53C29

MATHEMATICS | SPACES | INVARIANTS | METRICS | EXCEPTIONAL HOLONOMY | CONFORMAL HOLONOMY | DIFFERENTIAL-EQUATIONS | CLASSIFICATION | PARABOLIC GEOMETRIES | POINCARE-EINSTEIN MANIFOLDS | CONNECTIONS | Mathematics - Differential Geometry | 53A20 | 53A30 | 58J70 | 32V05 | 53B15 | 58D19 | 53C29

Journal Article

Journal of the Institute of Mathematics of Jussieu, ISSN 1474-7480, 09/2018, Volume 17, Issue 4, pp. 853 - 912

... $\unicode[STIX]{x2202}M$ has dimension $n$ even. Its definition depends on the choice of metric $h_{0}$ on $\unicode[STIX]{x2202}M...

differential geometry | conformal structures | global analysis | renormalized volume | analysis on manifolds | Poincaré-Einstein metrics | THEOREM | METRICS | FORMULA | MATHEMATICS | TENSOR | EINSTEIN | Poincare-Einstein metrics | MANIFOLDS | ELLIPTIC-EQUATIONS | GEOMETRY | Nonlinear equations | Linear equations | Reciprocity | Manifolds (mathematics)

differential geometry | conformal structures | global analysis | renormalized volume | analysis on manifolds | Poincaré-Einstein metrics | THEOREM | METRICS | FORMULA | MATHEMATICS | TENSOR | EINSTEIN | Poincare-Einstein metrics | MANIFOLDS | ELLIPTIC-EQUATIONS | GEOMETRY | Nonlinear equations | Linear equations | Reciprocity | Manifolds (mathematics)

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2014, Volume 63, Issue 1, pp. 119 - 163

On conformally compact manifolds of arbitrary signature, we use conformal geometry to identify a natural (and very general) class of canonical boundary...

Geometry | Riemann manifold | Tensors | Algebra | Tractors | Infinity | Mathematics | Laplacians | Signatures | Curvature | Conformally compact | Poincaré-Einstein | AdS/CFT | Conformal harmonics | Q-curvature | Scattering | Holography | Differential forms | Poisson transform | Poincare-Einstein | conformal harmonics | INVARIANT POWERS | LAPLACIAN | INFINITY | MATHEMATICS | ORIGINS | COHOMOLOGY | scattering | EINSTEIN-METRICS | holography | WAVE-EQUATION | conformally compact | OPERATORS

Geometry | Riemann manifold | Tensors | Algebra | Tractors | Infinity | Mathematics | Laplacians | Signatures | Curvature | Conformally compact | Poincaré-Einstein | AdS/CFT | Conformal harmonics | Q-curvature | Scattering | Holography | Differential forms | Poisson transform | Poincare-Einstein | conformal harmonics | INVARIANT POWERS | LAPLACIAN | INFINITY | MATHEMATICS | ORIGINS | COHOMOLOGY | scattering | EINSTEIN-METRICS | holography | WAVE-EQUATION | conformally compact | OPERATORS

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 2010, Volume 60, Issue 10, pp. 1558 - 1575

.... In the case of a Poincaré–Einstein metric the doubling gives rise to an almost Einstein manifold with hypersurface singularity...

Totally umbilic and minimal submanifolds | Poincaré–Einstein metrics | Almost Einstein structures | Conformal holonomy | Conformal geometry | Poincaré-Einstein metrics | MATHEMATICS | Poincare-Einstein metrics | CURVATURE | METRICS | PHYSICS, MATHEMATICAL

Totally umbilic and minimal submanifolds | Poincaré–Einstein metrics | Almost Einstein structures | Conformal holonomy | Conformal geometry | Poincaré-Einstein metrics | MATHEMATICS | Poincare-Einstein metrics | CURVATURE | METRICS | PHYSICS, MATHEMATICAL

Journal Article

Differential Geometry and its Applications, ISSN 0926-2245, 2011, Volume 29, Issue 3, pp. 440 - 462

Almost Einstein manifolds are conformally Einstein up to a scale singularity, in general. This notion comes from conformal tractor calculus. In the current...

Almost Einstein spaces | Poincaré–Einstein space | Poincaré-Einstein space | MATHEMATICS | MATHEMATICS, APPLIED | Poincare-Einstein space | METRICS | CURVATURE | CONFORMAL GEOMETRY | Family | Manifolds | Singularities | Tractors | Mathematical analysis | Differential equations | Lie groups | Calculus | Boundaries

Almost Einstein spaces | Poincaré–Einstein space | Poincaré-Einstein space | MATHEMATICS | MATHEMATICS, APPLIED | Poincare-Einstein space | METRICS | CURVATURE | CONFORMAL GEOMETRY | Family | Manifolds | Singularities | Tractors | Mathematical analysis | Differential equations | Lie groups | Calculus | Boundaries

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2010, Volume 12, Issue 4, pp. 629 - 659

...; they are Einstein on an open dense subspace and, in general, have a conformal scale singularity set that is a conformal infinity for the Einstein metric...

tractor calculus | PoincaréEinstein spaces | almost Einstein spaces | PoincaréEinstein manifolds | asymptotically hyperbolic | Conformal differential geometry | conformal holonomy | constant mean curvature hypersurfaces | MATHEMATICS, APPLIED | Poincare-Einstein spaces | METRICS | PRESCRIBED CONFORMAL INFINITY | FORMULA | Q-CURVATURE | LAPLACIAN | MATHEMATICS | Poincare-Einstein manifolds | TRACTORS

tractor calculus | PoincaréEinstein spaces | almost Einstein spaces | PoincaréEinstein manifolds | asymptotically hyperbolic | Conformal differential geometry | conformal holonomy | constant mean curvature hypersurfaces | MATHEMATICS, APPLIED | Poincare-Einstein spaces | METRICS | PRESCRIBED CONFORMAL INFINITY | FORMULA | Q-CURVATURE | LAPLACIAN | MATHEMATICS | Poincare-Einstein manifolds | TRACTORS

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 2010, Volume 60, Issue 2, pp. 182 - 204

...; Einstein metrics, Poincaré–Einstein metrics, and compactifications of certain Ricci-flat asymptotically locally Euclidean structures are special cases...

Poincaré–Einstein manifolds | Conformal differential geometry | Einstein manifolds | Poincaré-Einstein manifolds | LAPLACIAN | MATHEMATICS | COHOMOLOGY | Poincare-Einstein manifolds | AMBIENT OBSTRUCTION TENSOR | METRICS | PHYSICS, MATHEMATICAL | CONFORMALLY INVARIANT POWERS | DEFORMATION | Q-CURVATURE

Poincaré–Einstein manifolds | Conformal differential geometry | Einstein manifolds | Poincaré-Einstein manifolds | LAPLACIAN | MATHEMATICS | COHOMOLOGY | Poincare-Einstein manifolds | AMBIENT OBSTRUCTION TENSOR | METRICS | PHYSICS, MATHEMATICAL | CONFORMALLY INVARIANT POWERS | DEFORMATION | Q-CURVATURE

Journal Article

13.
Full Text
Escobar–Yamabe compactifications for Poincaré–Einstein manifolds and rigidity theorems

Advances in Mathematics, ISSN 0001-8708, 02/2019, Volume 343, pp. 16 - 35

Let (Xn,g+)(n≥3) be a Poincaré–Einstein manifold which is C3,α conformally compact with conformal infinity (∂X,[gˆ]). On the conformal compactification...

Poincaré–Einstein manifold | Yamabe constant | Rigidity | MATHEMATICS | MEAN-CURVATURE | BOUNDARY | Poincaro-Einstein manifold | SCALAR-FLAT METRICS

Poincaré–Einstein manifold | Yamabe constant | Rigidity | MATHEMATICS | MEAN-CURVATURE | BOUNDARY | Poincaro-Einstein manifold | SCALAR-FLAT METRICS

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 06/2018, Volume 128, pp. 48 - 57

In this paper, we discuss the mass aspect tensor and the rigidity of an asymptotically Poincaré-Einstein (APE) 4-manifold with harmonic curvature. We prove...

Mass aspect tensor | Rigidity | Asymptotically Poincaré-Einstein manifold | Harmonic curvature | MATHEMATICS | Asymptotically Poincare-Einstein manifold | METRICS | MANIFOLDS | PHYSICS, MATHEMATICAL

Mass aspect tensor | Rigidity | Asymptotically Poincaré-Einstein manifold | Harmonic curvature | MATHEMATICS | Asymptotically Poincare-Einstein manifold | METRICS | MANIFOLDS | PHYSICS, MATHEMATICAL

Journal Article

Conformal Geometry and Dynamics, ISSN 1088-4173, 03/2011, Volume 15, Issue 3, pp. 20 - 43

...-Beltrami operator of the metric g and (g) is the scalar curvature of g. The operator P2 is called the conformal Laplacian or Yamabe operator. More generally, in GJMS...

Conformally invariant powers of Laplacian | Poincaré-Einstein metrics | Universality | Q-curvature | Renormalized volume

Conformally invariant powers of Laplacian | Poincaré-Einstein metrics | Universality | Q-curvature | Renormalized volume

Journal Article

Memoirs of the American Mathematical Society, ISSN 0065-9266, 05/2015, Volume 235, Issue 1106, pp. 1 - 106

We study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. We solve these Laplace-type boundary problems formally,...

Conformally compact | Conformal harmonics | Q-curvature | Scattering | Ads/cft | Holography | Differential forms | Poisson transform | Poincare-einstein | Poincare-Einstein | conformal harmonics | INVARIANT POWERS | SITTER | MASSIVE HIGHER SPINS | LAPLACIAN | INFINITY | MATHEMATICS | AdS/CFT | scattering | holography | WAVE-EQUATION | MANIFOLDS | conformally compact | OPERATORS

Conformally compact | Conformal harmonics | Q-curvature | Scattering | Ads/cft | Holography | Differential forms | Poisson transform | Poincare-einstein | Poincare-Einstein | conformal harmonics | INVARIANT POWERS | SITTER | MASSIVE HIGHER SPINS | LAPLACIAN | INFINITY | MATHEMATICS | AdS/CFT | scattering | holography | WAVE-EQUATION | MANIFOLDS | conformally compact | OPERATORS

Journal Article

2000, Advanced series on theoretical physical science, ISBN 9789810238889, Volume 7, xxi, 418

Book

Letters in Mathematical Physics, ISSN 0377-9017, 5/2019, Volume 109, Issue 5, pp. 1247 - 1256

In this paper, we give an optimal inequality relating the relative Yamabe invariant of a certain compactification of a conformally compact Poincaré–Einstein...

Geometry | 53C24 | Theoretical, Mathematical and Computational Physics | Complex Systems | Uniqueness | Group Theory and Generalizations | Differential Geometry | Physics | Yamabe invariants | 53C80 | Poincaré-Einstein manifold | Poincare-Einstein manifold | PHYSICS, MATHEMATICAL

Geometry | 53C24 | Theoretical, Mathematical and Computational Physics | Complex Systems | Uniqueness | Group Theory and Generalizations | Differential Geometry | Physics | Yamabe invariants | 53C80 | Poincaré-Einstein manifold | Poincare-Einstein manifold | PHYSICS, MATHEMATICAL

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 02/2012, Volume 285, Issue 2‐3, pp. 150 - 163

...Introduction A conformal structure on a smooth manifold M is an equivalence class of Riemannian metric tensors, in which two metrics g and \documentclass...

normal conformal Killing forms | collapsing sphere products | Cartan and tractor calculus | special Einstein products | conformal holonomy | almost Einstein structures | MSC 53A30 | 53C25 | Conformal geometry | 53C29 | Special Einstein products | Almost Einstein structures | Conformal holonomy | Collapsing sphere products | Normal conformal Killing forms | MATHEMATICS | POINCARE-EINSTEIN MANIFOLDS

normal conformal Killing forms | collapsing sphere products | Cartan and tractor calculus | special Einstein products | conformal holonomy | almost Einstein structures | MSC 53A30 | 53C25 | Conformal geometry | 53C29 | Special Einstein products | Almost Einstein structures | Conformal holonomy | Collapsing sphere products | Normal conformal Killing forms | MATHEMATICS | POINCARE-EINSTEIN MANIFOLDS

Journal Article

Russian Physics Journal, ISSN 1064-8887, 8/2009, Volume 52, Issue 8, pp. 816 - 822

Relativistic geometromechanics is developed whose kinematics in the quantum period of the Universe is significantly modified as compared with that of canonical...

Condensed Matter Physics | Nuclear Physics, Heavy Ions, Hadrons | Optics, Optoelectronics, Plasmonics and Optical Devices | Theoretical, Mathematical and Computational Physics | relativistic geometromechanics, Universe, relativistic Poincaré | Physics, general | Einstein mechanics | Physics | Relativistic geometromechanics, Universe, relativistic Poincaré | Universe | relativistic Poincare - Einstein mechanics | relativistic geometromechanics | PHYSICS, MULTIDISCIPLINARY

Condensed Matter Physics | Nuclear Physics, Heavy Ions, Hadrons | Optics, Optoelectronics, Plasmonics and Optical Devices | Theoretical, Mathematical and Computational Physics | relativistic geometromechanics, Universe, relativistic Poincaré | Physics, general | Einstein mechanics | Physics | Relativistic geometromechanics, Universe, relativistic Poincaré | Universe | relativistic Poincare - Einstein mechanics | relativistic geometromechanics | PHYSICS, MULTIDISCIPLINARY

Journal Article

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