Resumen de Geometric elliptic functionals and mean curvature

Luis José Alías Linares , Jorge Herbert S. de Lira, Marco Rigoli

• We introduce an extended notion of mean curvature for graphs via the Euler-Lagrange equation of a geometric elliptic functional. We then draw some geometric conclusions for Killing graphs with prescribed weighted and anisotropic mean curvatures with the aid of a general form of the weak maximum principle and a sufficient condition for an appropriate notion of parabolicity.