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  -