On two-dimensional immersions of prescribed mean curvature in Rⁿ

2005/04/05 by Matthias Bergner, Bergner, Matthias, Steffen Froehlich +1 · 1 citation
Engineering · Mathematics · #Elasticity and Material Modeling #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #math.DG #msc:35J60 #msc:53A07 #msc:53A10

paper · pdf · doi:10.48550/arxiv.math/0504079

12 pages

arxiv created 2005/04/05 · arxiv updated 2009/12/01

Abstract

We consider two-dimensional immersions of disc-type in Rⁿ. We focus well known classical concepts and study the nonlinear elliptic systems of such mappings. Using an Osserman-type condition we give a priori-estimates of the principle curvatures for certain graphs in R⁴ with prescribed mean curvature.

Cited by

• Curvature estimates for graphs with prescribed mean curvature and flat normal bundle

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