Positive mass and Dirac operators on weighted manifolds and smooth metric measure spaces

Autor:	Law, Michael B., Lopez, Isaac M., Santiago, Daniel
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	We establish a weighted positive mass theorem which unifies and generalizes results of Baldauf--Ozuch and Chu--Zhu. Our result is in fact equivalent to the usual positive mass theorem, and can be regarded as a positive mass theorem for smooth metric measure spaces. We also study Dirac operators on certain warped product manifolds associated to smooth metric measure spaces. Applications of this include, among others, an alternative proof for a special case of our positive mass theorem, eigenvalue bounds for the Dirac operator on closed spin manifolds, and a new way to understand the weighted Dirac operator using warped products. Comment: 19 pages; references added, edited for readability
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.15441 Zobrazit plný text záznamu View this record from Arxiv