TL;DR
This paper investigates bounds on the second fundamental form of properly immersed self-shrinkers with bounded mean curvature and explores implications for gap and compactness results in geometric analysis.
Contribution
It provides new integral and pointwise bounds on the second fundamental form for a class of self-shrinkers with bounded mean curvature, advancing understanding of their geometric properties.
Findings
Established bounds on the second fundamental form.
Derived gap results for self-shrinkers.
Proved compactness theorems under bounded HA conditions.
Abstract
We study integral and pointwise bounds on the second fundamental form of properly immersed self-shrinkers with boundedHA. As applications, we discuss gap and compactness results for self-shrinkers.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Point processes and geometric inequalities