Remark on the Limit Case of Positive Mass Theorem for Manifolds with Inner Boundary
| dc.creator | Kim, Eui Chul | |
| dc.date | 2003-05-19 | |
| dc.date.accessioned | 2026-07-07T04:58:06Z | |
| dc.date.available | 2026-07-07T04:58:06Z | |
| dc.description | In [5] Herzlich proved a new positive mass theorem for Riemannian 3-manifolds $(N, g)$ whose mean curvature of the boundary allows some positivity. In this paper we study what happens to the limit case of the theorem when, at a point of the boundary, the smallest positive eigenvalue of the Dirac operator of the boundary is strictly larger than one-half of the mean curvature (in this case the mass $m(g)$ must be strictly positive). We prove that the mass is bounded from below by a positive constant $c(g), m(g) \geq c(g)$, and the equality $m(g) = c(g)$ holds only if, outside a compact set, $(N, g)$ is conformally flat and the scalar curvature vanishes. The constant $c(g)$ is uniquely determined by the metric $g$ via a Dirac-harmonic spinor. | |
| dc.description | 12 pages, latex2e | |
| dc.identifier | https://arxiv.org/abs/math/0305263 | |
| dc.identifier | http://arxiv.org/abs/math/0305263 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67504 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C27; 83C40 | |
| dc.title | Remark on the Limit Case of Positive Mass Theorem for Manifolds with Inner Boundary | |
| dc.type | text |