Mass functions of a compact manifold

JOURNAL OF GEOMETRY AND PHYSICS

卷:154

Article

Hermann, Andreas¹  Humbert, Emmanuel² 

[1] Univ Potsdam, Inst Math, Karl Liebknecht Str 24-25, D-14476 Potsdam, Germany

[2] Univ Tours, IDP, Parc Grandmont, F-37200 Tours, France

关键词: Yamabe operator;    Yamabe invariant;    Surgery;    Positive mass theorem;   

DOI  :  10.1016/j.geomphys.2020.103650

来源: Elsevier

【 摘 要 】

Let M be a compact manifold of dimension n. In this paper, we introduce the Mass Function a >= 0 bar right arrow X-+(M)(a) (resp. a >= 0 bar right arrow X--(M)(a)) which is defined as the supremum (resp. infimum) of the masses of all metrics on M whose Yamabe constant is larger than a and which are flat on a ball of radius 1 and centered at a point p is an element of M. Here, the mass of a metric flat around p is the constant term in the expansion of the Green function of the conformal Laplacian at p. We show that these functions are well defined and have many properties which allow to obtain applications to the Yamabe invariant (i.e. the supremum of Yamabe constants over the set of all metrics on M). (C) 2020 Published by Elsevier B.V.

【 授权许可】

Free