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Contracting Self-similar Solutions of Nonhomogeneous Curvature Flows

Journal Article


Abstract


  • A recent article (Li and Lv, J Geom Anal 30:417–447, 2020) 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.

Publication Date


  • 2021

Citation


  • McCoy, J. A. (2021). Contracting Self-similar Solutions of Nonhomogeneous Curvature Flows. Journal of Geometric Analysis, 31(6), 6410-6426. doi:10.1007/s12220-020-00538-4

Scopus Eid


  • 2-s2.0-85093974698

Start Page


  • 6410

End Page


  • 6426

Volume


  • 31

Issue


  • 6

Abstract


  • A recent article (Li and Lv, J Geom Anal 30:417–447, 2020) 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.

Publication Date


  • 2021

Citation


  • McCoy, J. A. (2021). Contracting Self-similar Solutions of Nonhomogeneous Curvature Flows. Journal of Geometric Analysis, 31(6), 6410-6426. doi:10.1007/s12220-020-00538-4

Scopus Eid


  • 2-s2.0-85093974698

Start Page


  • 6410

End Page


  • 6426

Volume


  • 31

Issue


  • 6