maximize
[1] U. Clarenz. A stability criterion for extremals of elliptic parametric functionals. Pacific Journal of Mathematics, 208(2):231-242, 2003.
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In this paper we consider parametric integrals F with elliptic integrands depending on the surface normal. The main result is a stability criterion for F -extremal immersions, containing the result of Barbosa and do Carmo [?] 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 F-extremals is topologically equivalent to a holomorphic function.