Conformal geometry of embedded manifolds with boundary from universal holographic formulæ
Cargando...
Archivos
Fecha
2021-06
Autores
Profesor/a Guía
Facultad/escuela
Idioma
en
Título de la revista
ISSN de la revista
Título del volumen
Editor
Academic Press Inc.
Nombre de Curso
Licencia CC
Licencia CC
Resumen
For an embedded conformal hypersurface with boundary, we construct critical order local invariants and their canonically associated differential operators. These are obtained holographically in a construction that uses a singular Yamabe problem and a corresponding minimal hypersurface with boundary. They include an extrinsic Q-curvature for the boundary of the embedded conformal manifold and, for its interior, the Q-curvature and accompanying boundary transgression curvatures. This gives universal formulæ for extrinsic analogs of Branson Q-curvatures that simultaneously generalize the Willmore energy density, including the boundary transgression terms required for conformal invariance. It also gives extrinsic conformal Laplacian power type operators associated with all these curvatures. The construction also gives formulæ for the divergent terms and anomalies in the volume and hyper-area asymptotics determined by minimal hypersurfaces having boundary at the conformal infinity. A main feature is the development of a universal, distribution-based, boundary calculus for the treatment of these and related problems. © 2021
Notas
Indexación Scopus
Palabras clave
Parabolic Geometry, Pseudoconvex, Holonomy, Conformal geometry, Embedded manifolds with boundary
Citación
Advances in Mathematics Volume 384, 25 June 2021, Article number 107700
DOI
10.1016/j.aim.2021.107700