Curvature estimates for minimal submanifolds of higher codimension
Y. L. Xin, Ling Yang
TL;DR
This paper extends curvature estimates for minimal submanifolds to higher codimensions using the Gauss map, generalizing previous results and improving Bernstein-type theorems.
Contribution
It introduces generalized curvature estimates for minimal submanifolds of higher codimension via the Gauss map, broadening the scope of classical results.
Findings
Generalized curvature estimates for higher codimension
Extension of Schoen-Simon-Yau and Ecker-Huisken results
Improved Bernstein-type theorem for minimal submanifolds
Abstract
We derive curvature estimates for minimal submanifolds in Euclidean space for arbitrary dimension and codimension via Gauss map. Thus, Schoen-Simon-Yau's results and Ecker-Huisken's results are generalized to higher codimension. In this way we improve Hildebrandt-Jost-Widman's result for the Bernstein type theorem.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research