Mean value surfaces with prescribed curvature form

Guida PARAMETRIC SURFACES WITH PRESCRIBED MEAN CURVATURE

This article contains an overview on some old and new problems concerning two-dimensional parametric surfaces in R3 with prescribed mean curvature. Part of this exposition has constituted the subject of a series of lectures held by the first author at the Department of Mathematics of the University of Torino, during the Third Turin Fortnight on Nonlinear Analysis (September 23-28, 2001).

On Surfaces of Prescribed Weighted Mean Curvature

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 ...

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 surfaces and surfaces of prescribed mean curvature. We first prove enclosure theorems in R for such surfaces in cylindrical boundary configurations. Then we derive a general second variation formula for the anisotropic surfac...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Finite element approximations to surfaces of prescribed variable mean curvature

We give an algorithm for finding finite element approximations to surfaces of prescribed variable mean curvature, which span a given boundary curve. We work in the parametric setting and prove optimal estimates in the H 1 norm. The estimates are verified computationally. Mathematics Subject Classification (1991): 65N30 · 49Q05 · 53A10