The Dirichlet-to-Neumann Map for Poincar\'e-Einstein Fillings

Autor:	Blitz, Samuel, Gover, A. Rod, Kopiński, Jarosław, Waldron, Andrew
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 53C18 53A55 53C21 58J32
Druh dokumentu:	Working Paper
Popis:	We study the non-linear Dirichlet-to-Neumann map for the Poincar\'e-Einstein filling problem. For even dimensional manifolds we describe the range of this non-local map in terms of a natural rank two tensor along the boundary determined by the Poincar\'e-Einstein metric. This tensor is proportional to the variation of renormalized volume along a path of Poincar\'e-Einstein metrics. We show that it has an explicit formula and is the unique, natural conformal hypersurface invariant of transverse order equaling the boundary dimension. We also construct such conformally invariant Dirichlet-to-Neumann tensors for Poincar\'e-Einstein fillings for odd dimensional manifolds with conformally flat boundary. Comment: 18 pages LaTeX
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2307.08470 Zobrazit plný text záznamu View this record from Arxiv