On Deformable Minimal Hypersurfaces in Space Forms
Andreas Savas-Halilaj
TL;DR
This paper classifies minimal hypersurfaces with zero Gauss-Kronecker curvature in 4D space forms, providing new insights into their local and complete structures under curvature constraints.
Contribution
It completes the local classification of such hypersurfaces and extends to classify complete cases with scalar curvature bounded below.
Findings
Complete local classification of minimal hypersurfaces with vanishing Gauss-Kronecker curvature.
Classification of complete minimal hypersurfaces with scalar curvature bounded from below.
New structural insights into hypersurfaces in 4D space forms.
Abstract
The aim of this paper is to complete the local classification of minimal hypersurfaces with vanishing Gauss-Kronecker curvature in a 4-dimensional space form. Moreover, we give a classification of complete minimal hypersurfaces with vanishing Gauss-Kronecker curvature and scalar curvature bounded from below.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds