Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (1): 107-112.doi: 10.1016/S0252-9602(10)60026-4

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FINITENESS OF HIGHER CODIMENSIONAL DISJOINT MINIMAL GRAPHS

 DONG Yu-Xin, JI Qing-Chun, ZHANG Wei   

  1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China
  • Received:2007-12-30 Revised:2008-10-10 Online:2010-01-20 Published:2010-01-20
  • Supported by:

    The first author is supported by zhongdian grant of NSFC (A010501) and NSFC-NSF (1081112053)  and the second author is supported by  NSFC (10701025).

Abstract:

We estimate the number of disjoint open subsets in Rn, which can support area-decreasing minimal graphs. This result generalizes the related results of Li-Wang and Tkachev for minimal hypersurfaces to higher codimensional case.

Key words: area-decreasing, volume estimate, disjoint minimal graph

CLC Number: 

  • 53A10
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