A stability criterion for extremals of elliptic parametric functionals

Ulrich Clarenz

Vol. 208 (2003), No. 2, 231–242

DOI: 10.2140/pjm.2003.208.231

Abstract

In this paper we consider parametric integrals with elliptic integrands depending on the surface normal. The main result is a stability criterion for extremal immersions of those functionals, containing a result of Barbosa and do Carmo for minimal surfaces as a special case. Using similar techniques we are also able to show a condition for instability. The last section contains a simple proof of the fact that the surface normal of extremals of parametric integrals is topologically equivalent to a holomorphic function.

Milestones

Received: 29 August 2001

Published: 1 February 2003