Nonexistence results and convex hull property for maximal surfaces in Minkowski three-space

Rosa Maria Barreiro Chaves and Leonor Ferrer

Vol. 231 (2007), No. 1, 1–26

DOI: 10.2140/pjm.2007.231.1

Abstract

We study properly immersed maximal surfaces with nonempty boundary and singularities in three-dimensional Minkowski space. We use the maximum principle and scaling arguments to obtain nonexistence results for these surfaces when the boundary is planar. We also give sufficient conditions for such surfaces to satisfy the convex hull property.

Keywords

maximal surfaces

Mathematical Subject Classification 2000

Primary: 53C50

Secondary: 53C42, 53C80

Milestones

Received: 15 December 2005

Accepted: 10 April 2006

Published: 1 May 2007