Boundary calculus for conformally compact manifolds

DOI10.1512/iumj.2014.63.5057zbMath1310.53060arXiv1104.2991OpenAlexW2962763441MaRDI QIDQ5174982

A. Rod Gover, Andrew K. Waldron

Publication date: 19 February 2015

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.2991

zbMATH Keywords

scatteringdifferential formsholographyAdS/CFTPoisson transformQ-curvatureconformally compact manifoldsPoincaré-Einstein manifoldsconformally harmonics

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) PDEs in connection with quantum mechanics (35Q40) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Applications of local differential geometry to the sciences (53B50) Differential invariants (local theory), geometric objects (53A55) Other connections (53B15) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items

On conformal higher spin wave operators ⋮ Shift operators, residue families and degenerate Laplacians ⋮ Boundary values of mixed-symmetry massless fields in AdS space ⋮ Tractor geometry of asymptotically flat spacetimes ⋮ The massive wave equation in asymptotically AdS spacetimes ⋮ The holographic Hadamard condition on asymptotically anti-de Sitter spacetimes ⋮ Variational calculus for hypersurface functionals: singular Yamabe problem Willmore energies ⋮ A sharp characterization of the Willmore invariant ⋮ Volume renormalization for singular Yamabe metrics ⋮ Conformal fundamental forms and the asymptotically Poincare-Einstein condition ⋮ Scattering on singular Yamabe spaces ⋮ Higher-order singletons, partially massless fields, and their boundary values in the ambient approach ⋮ Massive higher spins from BRST and tractors ⋮ Renormalized volumes with boundary ⋮ Asymptotic shear and the intrinsic conformal geometry of null-infinity ⋮ Conformal geometry of embedded manifolds with boundary from universal holographic formulæ ⋮ Renormalized volume ⋮ A calculus for higher spin interactions ⋮ Conformal boundary operators, \(T\)-curvatures, and conformal fractional Laplacians of odd order ⋮ A calculus for conformal hypersurfaces and new higher Willmore energy functionals ⋮ Conformal symmetry breaking differential operators on differential forms ⋮ Bernstein-Sato identities and conformal symmetry breaking operators ⋮ Poincaré–Einstein holography for forms via conformal geometry in the bulk ⋮ Residue families, singular Yamabe problems and extrinsic conformal Laplacians ⋮ PARABOLIC COMPACTIFICATION OF HOMOGENEOUS SPACES ⋮ Einstein gravity as a gauge theory for the conformal group