About the mass of certain second order elliptic operators
- 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.
Author details: | Andreas Hermann, Emmanuel Humbert |
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DOI: | https://doi.org/10.1016/j.aim.2016.03.008 |
ISSN: | 0001-8708 |
ISSN: | 1090-2082 |
Title of parent work (English): | Advances in mathematics |
Publisher: | Elsevier |
Place of publishing: | San Diego |
Publication type: | Article |
Language: | English |
Year of first publication: | 2016 |
Publication year: | 2016 |
Release date: | 2020/03/22 |
Tag: | Positive mass theorem; Surgery; Yamabe operator |
Volume: | 294 |
Number of pages: | 38 |
First page: | 596 |
Last Page: | 633 |
Funding institution: | Deutsche Forschungsgemeinschaft [HE 6908/1-1]; Agence Nationale de la Recherche [ANR-10-BLAN 0105, ANR-12-BS01-012-01] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |