Mass functions of a compact manifold
- 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).
| Author details: | Andreas Hermann, Emmanuel Humbert |
|---|---|
| DOI: | https://doi.org/10.1016/j.geomphys.2020.103650 |
| ISSN: | 0393-0440 |
| ISSN: | 1879-1662 |
| Title of parent work (English): | Journal of geometry and physics : JGP |
| Publisher: | Elsevier |
| Place of publishing: | Amsterdam [u.a.] |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2020/04/18 |
| Publication year: | 2020 |
| Release date: | 2023/04/19 |
| Tag: | Yamabe invariant; Yamabe operator; positive mass theorem; surgery |
| Volume: | 154 |
| Article number: | 103650 |
| Number of pages: | 14 |
| Funding institution: | project THESPEGE (APR IA), Region Centre-Val de Loire, France; Deutsche; Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [SPP 2026] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Green Open-Access |
