Document Type

Article

Publication Date

1-31-2010

Publication Title

Indiana University Mathematics Journal

Abstract

In the paper [13] we proved that the only stable C 2 minimal surfaces in the first Heisenberg group H 1 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 em-bedded minimal surfaces in H 1 with empty characteristic locus. We prove that every such a surface without boundary must be a vertical plane. This result represents a sub-Riemannian coun-terpart of the classical theorems of Fischer-Colbrie and Schoen, [16], and do Carmo and Peng, [15], and answers a question posed by Lei Ni.

DOI

10.1512/iumj.2010.59.4291

Included in

Mathematics Commons

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