Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (5): 1176-1180.

• Articles • Previous Articles     Next Articles

A Remark on the Convexity of Hypersurface with Prescribed Curvature Equations

 XU Jin-Ju   

  1. Department of Mathematics, University of Science and Technology of China, Hefei 230026|School of Mathematics and Science, Qufu Normal University, Shandong Qufu 273165
  • Received:2010-01-15 Revised:2011-03-06 Online:2011-10-25 Published:2011-10-25
  • Supported by:

    国家自然科学基金(10671186)资助

Abstract:

In this article, the author investigates the solution surface of the prescribed curvature equation Skλ{hij})(X),=\, f(X),\, \forall XM\subsetRn+1. It is proved that the solution surface M of the prescribed curvature equation in Rn+1 is convex under the condition that the second fundamental form hij of M is semi-positive definite on the boundary ∂M. The author  makes use of Hamilton tensor maximum principle to prove this result. As a consequence, the convexity for the solution surface of constant mean curvature in Rn+1 is easily obtained.

Key words: Convexity, Curvature equation, Maximum principle

CLC Number: 

  • 35J60
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