On Surfaces of Prescribed Weighted Mean Curvature

Details On Surfaces of Prescribed Weighted Mean Curvature On Surfaces of Prescribed Weighted Mean Curvature

2007-11-15

arxiv.org/abs/0711.2406v1

Mathematics

Differential Geometry

Scientific paper

Utilizing a weight matrix we study surfaces of prescribed weighted mean curvature which yield a natural generalisation to critical points of anisotropic surface energies. We first derive a differential equation for the normal of immersions with prescribed weighted mean curvature, generalising a result of Clarenz and von der Mosel. Next we study graphs of prescribed weighted mean curvature, for which a quasilinear elliptic equation is proved. Using this equation, we can show height and boundary gradient estimates. Finally, we solve the Dirichlet problem for graphs of prescribed weighted mean curvature.

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