A stability criterion for extremals of elliptic parametric functionals. (Q1880016)

The author considers the stability and instability of a given minimal surface. He considers parametric integrals \(\mathcal{F}\) with elliptic integrands depending on the normal surface. The main result is a stability criterion for \(\mathcal{F}\)-extremal immersions, containing a result of Barbosa and do Carmo as a special case. The last section contains a simple proof of the fact that the surface normal of \(\mathcal{F}\)-extremals is topologically equivalent to a holomorphic function.