On Surfaces of Prescribed Weighted Mean Curvature

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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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Differential Geometry, Analysis of PDEs, 53A10

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http://salesiana.dossiersoluciones.com/handle/123456789/142199

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0711.2406
 http://arxiv.org/abs/0711.2406

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arXiv