Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (5): 1269-1274.doi: 10.1016/S0252-9602(13)60079-X

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NEW SPECTRAL CHARACTERIZATIONS OF EXTREMAL HYPERSURFACES

 YANG Deng-Yun, XU Hong-Wei, FU Hai-Ping   

  1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China|Center of Mathematics Sciences, Zhejiang University, Hangzhou 310027, China|Department of Mathematics, Nanchang University, Nanchang 330031, China
  • Received:2012-02-05 Online:2013-09-20 Published:2013-09-20

Abstract:

Let M be a closed extremal hypersurface in Sn+1 with the same mean curva-ture of the Willmore torus Wm,n−m. We proved that if Specp(M) = Specp(Wm,n−m) for p = 0, 1, 2, then M is Wm,m.

Key words: spectrum, Laplace operator, extremal hypersurface

CLC Number: 

  • 53C25
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