The bernstein problem for embedded surfaces in the heisenberg group ℍ1

Donatella Danielli, Nicola Garofalo, Duy Minh Nhieu, Scott D. Pauls

研究成果: 雜誌貢獻期刊論文同行評審

16 引文 斯高帕斯(Scopus)

摘要

In the paper [13] we proved that the only stable C2 minimal surfaces in the first Heisenberg group ℍ1 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 C2 complete embedded minimal surfaces in ℍ1 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.

原文???core.languages.en_GB???
頁(從 - 到)563-594
頁數32
期刊Indiana University Mathematics Journal
59
發行號2
DOIs
出版狀態已出版 - 2010

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