Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (3): 644-651.

• Articles • Previous Articles     Next Articles

Isotropic p-surface Area Measure

 YU Wu-Yang   

  1. Institute of Management Decision &|Innovation, Hangzhou Dianzi University, Hangzhou 310018
  • Received:2009-06-05 Revised:2010-12-12 Online:2011-06-25 Published:2011-06-25
  • Supported by:

    国家自然科学基金(11001014)资助

Abstract:

This paper studies the minimal p-surface area of a given convex body among its affine transformations of the same volume. A double-sided estimate for the volume of the polar Lp-projection body of p-surface isotropic convex body is given, and the p-isoperimetric inequality is given with its reverse form. Finally, the stability of the p-surface isotropic position for 1≤p≤2 is given.

Key words: Isotropic measure, p-surface area, Lp-projection bodies, p-isoperimetric inequality

CLC Number: 

  • 52A40
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