Cabezas-Rivas, Esther and Miquel, Vicente (2009) Volume-preserving mean curvature flow of revolution hypersurfaces in a rotationally symmetric space. Mathematische Zeitschrift, Vol.261 (No.3). pp. 489-510. doi:10.1007/s00209-008-0333-6

Research output not available from this repository, contact author.

Request Changes to record.

Abstract

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 ≥ 0, the evolving hypersurface M t meets such tgh orthogonally, 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 lies on 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.

Item Type:	Journal Article
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Mathematische Zeitschrift
Publisher:	Springer
ISSN:	0025-5874
Official Date:	2009
Dates:	Date Event 2009 Published
Volume:	Vol.261
Number:	No.3
Page Range:	pp. 489-510
DOI:	10.1007/s00209-008-0333-6
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

Request changes or add full text files to a record

Repository staff actions (login required)

View Item