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Contraction of convex hypersurfaces by nonhomogeneous functions of curvature

Journal Article


Abstract


  • A recent article 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 $C^\infty$-topology.

Publication Date


  • 2020

Web Of Science Accession Number


Abstract


  • A recent article 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 $C^\infty$-topology.

Publication Date


  • 2020

Web Of Science Accession Number