Acta mathematica scientia,Series B ›› 1997, Vol. 17 ›› Issue (2): 129-142.

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DEFORMING CONVEX HYPERSURFACES BY THE LINEAR COMBINATION OF THE MEAN CURVATURE AND THE N-TH ROOT OF THE GAUSS-KRONECKER CURVATURE

Shen Yibing, Sheng Weimin   

  1. Dept. of Math., Hangzhou University, Hangzhou 510028, China
  • Received:1995-02-19 Online:1997-06-25 Published:1997-06-25
  • Supported by:
    Project supported by NNSFC and NSFZP.

Abstract: In this paper a flow of convex hypersurfaces in the Euclidean space by the linear combination of the mean curvature and the n-th root of the Gauss-Kronecker curvature is considererd. It is proved that such deforming convex hypersurfaces converge to a round sphere in the Huisken's sense.

Key words: curvature flow, mean curvature, Gauss-Kronecker curvature, convexity, hypersurface

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