Contraction of convex hypersurfaces by nonhomogeneous functions of curvature

Title: Contraction of convex hypersurfaces by nonhomogeneous functions of curvature
Creator: McCoy, James A.
Relation: ARC.DP180100431 http://purl.org/au-research/grants/arc/DP180100431
Relation: Journal of Evolution Equations Vol. 21, p. 2265-2291
Publisher Link: http://dx.doi.org/10.1007/s00028-021-00683-5
Publisher: Birkhaeuser Science
Resource Type: journal article
Date: 2021
Description: A recent article of Li and Lv considered contraction of convex hypersurfaces by certain nonhomogeneous functions of curvature, showing convergence to points in finite time in certain cases where the speed is a function of a degree-one homogeneous, concave and inverse concave function of the principle curvatures. In this article we extend the result to various other cases that are analogous to those considered in other earlier work, and we show that in all cases, where sufficient pinching conditions are assumed on the initial hypersurface, then under suitable rescaling the final point is asymptotically round and convergence is exponential in the C^∞-topology.
Subject: curvature flow; parabolic partial differential equation; hypersurface; mixed volume; axial symmetry
Identifier: http://hdl.handle.net/1959.13/1439031
Identifier: uon:40799
Identifier: ISSN:1424-3199
Language: eng
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