On two-dimensional immersions of prescribed mean curvature in R^n
Matthias Bergner, Steffen Froehlich
TL;DR
This paper investigates two-dimensional immersions with prescribed mean curvature in R^n, providing a priori curvature estimates for certain graphs in R^4 using an Osserman-type condition.
Contribution
It introduces new a priori curvature estimates for specific immersions with prescribed mean curvature in higher dimensions, extending classical concepts.
Findings
A priori estimates of principal curvatures for certain graphs in R^4
Application of Osserman-type condition to nonlinear elliptic systems
Advancement in understanding of curvature behavior in prescribed mean curvature immersions
Abstract
We consider two-dimensional immersions of disc-type in R^n. 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 R^4 with prescribed mean curvature.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Elasticity and Material Modeling