Stabilization technique applied to curve shortening flow in the plane
Hayk Mikayelyan
TL;DR
This paper applies Zelenjak's stabilization method to the planar mean curvature flow, deriving a new monotonicity formula specifically for star-shaped curves, advancing understanding of curve evolution in geometric analysis.
Contribution
It introduces a novel stabilization technique to the mean curvature flow in the plane, resulting in a new monotonicity formula for star-shaped curves.
Findings
Derived a new monotonicity formula for star-shaped curves
Extended Zelenjak's method to mean curvature flow in the plane
Enhanced understanding of curve evolution dynamics
Abstract
The method proposed by T. I. Zelenjak is applied to the mean curvature flow in the plane. A new type of monotonicity formula for star-shaped curves is obtained.
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