On Surfaces of Prescribed Weighted Mean Curvature
Differential Geometry
2007-11-16 v1 Analysis of PDEs
Abstract
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.
Keywords
Cite
@article{arxiv.0711.2406,
title = {On Surfaces of Prescribed Weighted Mean Curvature},
author = {Matthias Bergner and Jens Dittrich},
journal= {arXiv preprint arXiv:0711.2406},
year = {2007}
}