- Treffer 1 von 1
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.
| Verfasserangaben: | Andreas Hermann, Emmanuel Humbert |
|---|---|
| DOI: | https://doi.org/10.1016/j.aim.2016.03.008 |
| ISSN: | 0001-8708 |
| ISSN: | 1090-2082 |
| Titel des übergeordneten Werks (Englisch): | Advances in mathematics |
| Verlag: | Elsevier |
| Verlagsort: | San Diego |
| Publikationstyp: | Wissenschaftlicher Artikel |
| Sprache: | Englisch |
| Jahr der Erstveröffentlichung: | 2016 |
| Erscheinungsjahr: | 2016 |
| Datum der Freischaltung: | 22.03.2020 |
| Freies Schlagwort / Tag: | Positive mass theorem; Surgery; Yamabe operator |
| Band: | 294 |
| Seitenanzahl: | 38 |
| Erste Seite: | 596 |
| Letzte Seite: | 633 |
| Fördernde Institution: | Deutsche Forschungsgemeinschaft [HE 6908/1-1]; Agence Nationale de la Recherche [ANR-10-BLAN 0105, ANR-12-BS01-012-01] |
| Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer Review: | Referiert |
