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.

Authors