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Numerically computing the index of mean curvature flow self-shrinkers
Yakov Berchenko-Kogan
Surfaces that evolve by mean curvature flow develop singularities. These singularities can be modeled by self-shrinkers, surfaces that shrink by dilations under the flow. Singulari…
Bounds on the Index of Rotationally Symmetric Self-Shrinking Tori
Yakov Berchenko-Kogan
A closed surface evolving under mean curvature flow becomes singular in finite time. Near the singularity, the surface resembles a self-shrinker, a surface that shrinks by dilation…
The entropy of the Angenent torus is approximately 1.85122
Yakov Berchenko-Kogan
To study the singularities that appear in mean curvature flow, one must understand self-shrinkers, surfaces that shrink by dilations under mean curvature flow. The simplest example…
Yang-Mills Replacement
Yakov Berchenko-Kogan
We develop an analog of harmonic replacement in the gauge theory context. The idea behind harmonic replacement dates back to Schwarz and Perron. The technique, as introduced by Jos…