The rigidity of hypersurface in Euclidean space
Chunhe Li, Yanyan Xu
TL;DR
This paper explores the rigidity of hypersurfaces in Euclidean space, providing new proofs using energy methods and the maximal principle to deepen understanding of their geometric properties.
Contribution
It introduces a novel proof of hypersurface rigidity leveraging energy methods and the maximal principle, offering fresh insights into classical differential geometry.
Findings
New proof of hypersurface rigidity
Application of energy method and maximal principle
Enhanced understanding of geometric properties
Abstract
In the present paper, we revisit the rigidity of hypersurfaces in Euclidean space. We highlight Darboux equation and give new proof of rigidity of hypersurfaces by energy method and maximal principle.
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Taxonomy
TopicsNonlinear Waves and Solitons · Geometric Analysis and Curvature Flows · Advanced Differential Equations and Dynamical Systems