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math.DG2020
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…
math.DG2020★ 3 cited
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…
math.NA2020★ 3 cited
Charge-conserving hybrid methods for the Yang-Mills equations
Yakov Berchenko-Kogan, Ari Stern
The Yang-Mills equations generalize Maxwell's equations to nonabelian gauge groups, and a quantity analogous to charge is locally conserved by the nonlinear time evolution. Christi…