On minimal hypersurfaces in Euclidean spaces and Riemannian manifolds
Josef Mikes, Sergey Stepanov, Irina Tsyganok
TL;DR
This paper characterizes minimal and stable minimal hypersurfaces as hyperplanes in Euclidean spaces and as totally geodesic submanifolds in Riemannian manifolds, providing conditions for their identification.
Contribution
It introduces new criteria for identifying minimal hypersurfaces as hyperplanes or totally geodesic submanifolds in various geometric contexts.
Findings
Minimal hypersurfaces are hyperplanes in Euclidean spaces under certain conditions.
Stable minimal hypersurfaces are characterized as hyperplanes.
Minimal hypersurfaces are totally geodesic in Riemannian manifolds under specified conditions.
Abstract
This paper establishes the conditions under which minimal and stable minimal hypersurfaces are characterized as hyperplanes in Euclidean spaces and as totally geodesic submanifolds in Riemannian manifolds.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · 3D Shape Modeling and Analysis · Advanced Numerical Analysis Techniques