Maximum Principle for H-Surfaces in the Unit Cone and Dirichlet's Problem for their Equation in Central Projection

摘要

In the unit cone we establish a geometric maximum principle for H-surfaces, where its mean curvature is optimally bounded. Consequently, these surfaces cannot touch the conical boundary at interior points and have to approach transversally. By a nonlinear continuity method, we then solve the Dirichlet problem of the H-surface equation in central projection for Jordan-domains which are strictly convex in the following sense: On its whole boundary their associate cone admits rotated unit cones as solids of support, where represents a rotation in the Euclidean space. Thus we construct the unique H-surface with one-to-one central projection onto these domains bounding a given Jordan-contour with one-toone central projection.