- Title
- Contracting self-similar solutions of nonhomogeneous curvature flows
- Creator
- McCoy, James A.
- Relation
- ARC.DP180100431 http://purl.org/au-research/grants/arc/DP180100431
- Relation
- The Journal of Geometric Analysis Vol. 31, p. 6410-6426
- Publisher Link
- http://dx.doi.org/10.1007/s12220-020-00538-4
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2020
- Description
- A recent article by Li and Lv considered fully nonlinear contraction of convex hypersurfaces by certain nonhomogeneous functions of curvature, showing convergence to points in finite time in 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 consider self-similar solutions to these and related curvature flows that are not homogeneous in the principle curvatures, finding various situations where closed, convex curvature-pinched hypersurfaces contracting self-similarly are necessarily spheres.
- Subject
- curvature flow; parabolic partial differential equation; self-similar solution
- Identifier
- http://hdl.handle.net/1959.13/1439035
- Identifier
- uon:40798
- Identifier
- ISSN:1050-6926
- Rights
- This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s12220-020-00538-4
- Language
- eng
- Full Text
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