Constant mean curvature graphs in a strip of ℝ²

Rafael López

Vol. 206 (2002), No. 2, 359–373

DOI: 10.2140/pjm.2002.206.359

Abstract

We consider the Dirichlet problem for the constant mean curvature surface equation on domains of an infinite strip of the plane. We give sufficient conditions for the existence of smooth solutions provided that the boundary satisfies a certain exterior circle condition. A feature of the work is the use of pieces of nodoids as barriers to make C⁰ and C¹ a priori estimates respectively.

Milestones

Received: 4 January 2001

Published: 1 October 2002