TY  - JOUR
A1  - Hermann, Andreas
A1  - Humbert, Emmanuel
T1  - Mass functions of a compact manifold
JF  - 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
U6  - https://doi.org/10.1016/j.geomphys.2020.103650
SN  - 0393-0440
SN  - 1879-1662
VL  - 154
PB  - Elsevier
CY  - Amsterdam [u.a.]
ER  - 
TY  - JOUR
A1  - Hermann, Andreas
A1  - Humbert, Emmanuel
T1  - About the mass of certain second order elliptic operators
JF  - Advances in mathematics
N2  - Let (M, g) be a closed Riemannian manifold of dimension n >= 3 and let f is an element of C-infinity (M), such that the operator P-f := Delta g + f is positive. If g is flat near some point p and f vanishes around p, we can define the mass of P1 as the constant term in the expansion of the Green function of P-f at p. In this paper, we establish many results on the mass of such operators. In particular, if f := n-2/n(n-1)s(g), i.e. if P-f is the Yamabe operator, we show the following result: assume that there exists a closed simply connected non-spin manifold M such that the mass is non-negative for every metric g as above on M, then the mass is non-negative for every such metric on every closed manifold of the same dimension as M. (C) 2016 Elsevier Inc. All rights reserved.
KW  - Yamabe operator
KW  - Surgery
KW  - Positive mass theorem
Y1  - 2016
U6  - https://doi.org/10.1016/j.aim.2016.03.008
SN  - 0001-8708
SN  - 1090-2082
VL  - 294
SP  - 596
EP  - 633
PB  - Elsevier
CY  - San Diego
ER  -