The rigidity theorems of self shrinkers
Qi Ding, Y. L. Xin
TL;DR
This paper investigates the rigidity properties of self-shrinkers in geometric analysis, applying techniques from minimal submanifold theory to establish conditions under which self-shrinkers exhibit rigidity.
Contribution
It introduces new rigidity theorems for self-shrinkers based on point-wise and integral conditions on the second fundamental form.
Findings
Rigidity results for the squared norm of the second fundamental form.
Conditions under which self-shrinkers are uniquely determined.
Extension of minimal submanifold techniques to self-shrinkers.
Abstract
By using certain idea developed in minimal submanifold theory we study rigidity problem for self-shrinkers in the present paper. We prove rigidity results for squared norm of the second fundamental form of self-shrinkers, either under point-wise conditions or under integral conditions.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometric and Algebraic Topology