TY  - JOUR
A1  - Hermann, Andreas
A1  - Humbert, Emmanuel
T1  - Mass functions of a compact manifold
T2  - Journal of geometry and physics : JGP
N2  - 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).
KW  - Yamabe operator
KW  - Yamabe invariant
KW  - surgery
KW  - positive mass theorem
Y1  - 2020
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/58817
SN  - 0393-0440
SN  - 1879-1662
VL  - 154
PB  - Elsevier
CY  - Amsterdam [u.a.]
ER  -