Volume-preserving mean curvature flow of revolution hypersurfaces in a Rotationally Symmetric Space
| dc.creator | Cabezas-Rivas, Esther | |
| dc.creator | Miquel, Vicente | |
| dc.date | 2007-08-07 | |
| dc.date | 2008-03-26 | |
| dc.date.accessioned | 2026-07-07T09:28:11Z | |
| dc.date.available | 2026-07-07T09:28:11Z | |
| dc.description | In an ambient space with rotational symmetry around an axis (which include the Hyperbolic and Euclidean spaces), we study the evolution under the volume-preserving mean curvature flow of a revolution hypersurface M generated by a graph over the axis of revolution and with boundary in two totally geodesic hypersurfaces (tgh for short). Requiring that, for each time t, the evolving hypersurface M_t meets such tgh ortogonally, we prove that: a) the flow exists while M_t does not touch the axis of rotation; b) throughout the time interval of existence, b1) the generating curve of M_t remains a graph, and b2) the averaged mean curvature is double side bounded by positive constants; c) the singularity set (if non-empty) is finite and discrete along the axis; d) under a suitable hypothesis relating the enclosed volume to the n-volume of M, we achieve long time existence and convergence to a revolution hypersurface of constant mean curvature. | |
| dc.description | 24 pages. We have added some lines at the beginning explaining the notation, and clarified a little bit more the proofs of Proposition 1 and Theorems 5 and 10, the statements of Proposition 2 and Corollary 3 and an argument in Remark 1. We have also completed reference 18. A version of this paper will appear in Mathematische Zeitschrift | |
| dc.identifier | https://arxiv.org/abs/0708.0887 | |
| dc.identifier | http://arxiv.org/abs/0708.0887 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157365 | |
| dc.subject | Differential Geometry | |
| dc.title | Volume-preserving mean curvature flow of revolution hypersurfaces in a Rotationally Symmetric Space | |
| dc.type | text |