ON SURFACES OF PRESCRIBED F-MEAN CURVATURE

Hypersurfaces of prescribed weighted mean curvature, or F-mean curvature, are introduced as critical immersions of anisotropic surface energies, thus generalizing minimal sur-faces and surfaces of prescribed mean curvature. We first prove enclosure theorems in Rn+1 for such surfaces in cylindri-cal boundary configurations. Then we derive a general second variation formula for the anisotropic surface energies gener-alizing corresponding formulas of do Carmo for minimal sur-faces, and Sauvigny for prescribed mean curvature surfaces. Finally we prove that stable surfaces of prescribed F-mean curvature in R3 can be represented as graphs over a planar strictly convex domain Ω, if the given boundary contour in R3 is a graph over ∂Ω. 1. Introduction an