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Contraction of convex hypersurfaces by nonhomogeneous functions of curvature

Journal Article


Abstract


  • A recent article Li and Lv (J. Geom. Anal. 30: 417ā€“447, 2020) 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 Cāˆž-topology.

Publication Date


  • 2021

Citation


  • McCoy, J. A. (2021). Contraction of convex hypersurfaces by nonhomogeneous functions of curvature. Journal of Evolution Equations, 21(2), 2265-2291. doi:10.1007/s00028-021-00683-5

Scopus Eid


  • 2-s2.0-85103183380

Start Page


  • 2265

End Page


  • 2291

Volume


  • 21

Issue


  • 2

Abstract


  • A recent article Li and Lv (J. Geom. Anal. 30: 417ā€“447, 2020) 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 Cāˆž-topology.

Publication Date


  • 2021

Citation


  • McCoy, J. A. (2021). Contraction of convex hypersurfaces by nonhomogeneous functions of curvature. Journal of Evolution Equations, 21(2), 2265-2291. doi:10.1007/s00028-021-00683-5

Scopus Eid


  • 2-s2.0-85103183380

Start Page


  • 2265

End Page


  • 2291

Volume


  • 21

Issue


  • 2