The Bernstein Problem for Embedded Surfaces in the Heisenberg Group H

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题名:	The Bernstein Problem for Embedded Surfaces in the Heisenberg Group H
作者:	Danielli,D;Garofalo,N;Nhieu,DM;Pauls,SD
贡献者:	數學系
日期:	2010
上传时间:	2012-03-27 18:23:25 (UTC+8)
出版者:	國立中央大學
摘要:	In the paper [13] we proved that the only stable C(2) minimal surfaces in the first Heisenberg group HI which are graphs over some plane and have empty characteristic locus must be vertical planes. This result represents a sub-Riemannian version of the celebrated theorem of Bernstein. In this paper we extend the result in [13] to C(2) complete embedded minimal surfaces in HI with empty characteristic locus. We prove that every such a surface without boundary must be a vertical plane. This result represents a sub-Riemannian counterpart of the classical theorems of Fischer-Colbrie and Schoen, [16], and do Carmo and Peng, [15], and answers a question posed by Lei Ni.
關聯:	INDIANA UNIVERSITY MATHEMATICS JOURNAL
显示于类别:	[數學系] 期刊論文

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