Smooth compactness of self-shrinkers

Abstract

We prove a smooth compactness theorem for the space of embedded self-shrinkers in $\RR^3$. Since self-shrinkers model singularities in mean curvature flow, this theorem can be thought of as a compactness result for the space of all singularities and it plays an important role in studying generic mean curvature flow.

References in corpus (1)

• Evolution of curves and surfaces by mean curvature

Cited by in corpus (8)

• Generic mean curvature flow I; generic singularities
• On the self-shrinking systems in arbitrary codimension spaces
• Closed self-shrinking surfaces in ${\mathbb{R}}^3$ via the torus
• The rigidity theorems of self shrinkers
• Volume estimate about shrinkers
• Estimates for eigenvalues of $\mathfrak{L}$ operator on Self-Shrinkers
• The stability inequality for Ricci-flat cones
• A Bernstein type theorem for graphic self-shrinkers with flat normal bundle