The curve shortening problem associated to a density

2015/03/09 by Vicente Miquel, Miquel, Vicente, Francisco Viñado-Lereu +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1503.02429

Abstract

In ℝⁿ with a density e^ψ, we study the mean curvature flow associated to the density (ψ-mean curvature flow or ψMCF) of a hypersurface. The main results concern with the description of the evolution under ψMCF of a closed embedded curve in the plane with a radial density, and with a statement of subconvergence to a ψ-minimal closed curve in a surface under some general circumstances.

Citations

• Embedded self-similar shrinkers of genus 0

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• Gaussian Mean curvature flow
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