Scalar curvature and the relative capacity of geodesic balls

Autor:	Jauregui, Jeffrey L.
Rok vydání:	2020
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs
Zdroj:	Proc. Amer. Math. Soc., Vol 149, No. 11, (2021), pp. 4907--4921
Druh dokumentu:	Working Paper
Popis:	In a Riemannian manifold, it is well known that the scalar curvature at a point can be recovered from the volumes (areas) of small geodesic balls (spheres). We show the scalar curvature is likewise determined by the relative capacities of concentric small geodesic balls. This result has motivation from general relativity (as a complement to a previous study by the author of the capacity of large balls in an asymptotically flat manifold) and from weak definitions of nonnegative scalar curvature. It also motivates a conjecture (inspired by the famous volume conjecture of Gray and Vanhecke), regarding whether Euclidean-like behavior of the relative capacity on the small scale is sufficient to characterize a space as flat. Comment: 14 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2009.12394 Zobrazit plný text záznamu View this record from Arxiv