On 2-surfaces in R^4 and R^n

TL;DR

This paper generalizes curvature estimates for minimal graphs from three to higher dimensions and explores the geometry of surfaces in R^4, introducing concepts like normal torsion and curvature.

Contribution

It extends Heinz's curvature estimate to graphs in R^n with prescribed mean curvature and develops new geometric notions for immersions in R^4.

Findings

Generalized Heinz's curvature estimate to R^n

Introduced normal torsion and curvature for R^4 immersions

Analyzed minimal graphs in higher-dimensional Euclidean spaces

Abstract

In this overview report we generalize Erhard Heinz' curvature estimate for minimal graphs in R^3 to graphs in R^n of prescribed mean curvature. Secondly, we analyse these problems in the frame of the outer differential geometry which leads us to the notions of normal torsion and normal curvature for immersions in R^4.