More mixed volume preserving curvature flows

Title: More mixed volume preserving curvature flows
Creator: McCoy, James A.
Relation: Journal of Geometric Analysis Vol. 27, Issue 4, p. 3140-3165
Publisher Link: http://dx.doi.org/10.1007/s12220-017-9799-y
Publisher: Springer
Resource Type: journal article
Date: 2017
Description: We extend the results of McCoy (Calc Var Partial Differ Equ 24:131–154, 2005) to include several new cases where convex surfaces evolve to spheres under mixed volume preserving curvature flows, using recent results for unconstrained curvature flows and new regularity arguments in the constrained flow setting. We include results for speeds that are degree 1 homogeneous in the principal curvatures and indicate how, with sufficient curvature pinching conditions on the initial hypersurfaces, some results may be extended to speed homogeneous of degree α> 1. In particular, these extensions require lower speed bounds that are obtained here without using estimates for equations of porous medium type, in contrast to most previous work.
Subject: curvature flow; parabolic partial differential equation; hypersurface; mixed volume; axial symmetry
Identifier: http://hdl.handle.net/1959.13/1436996
Identifier: uon:40203
Identifier: ISSN:1050-6926
Language: eng
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