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Asymptotic behavior of a diffused interface volume-preserving mean curvature flow

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arxiv 2407.18868 v1 pith:DDYHO7M5 submitted 2024-07-26 math.AP math.DGmath.OC

Matteo Bonforte , Francesco Maggi , Daniel Restrepo This is my paper · ORCID
classification math.APmath.DGmath.OC
keywords diffusedcurvatureflowinterfacemeanvolume-preservingassumptionsasymptotic
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We consider a diffused interface version of the volume-preserving mean curvature flow in the Euclidean space, and prove, in every dimension and under natural assumptions on the initial datum, exponential convergence towards single "diffused balls".

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  1. Brakke inequality and the existence of Brakke-flow for volume preserving mean curvature flow

    math.AP 2025-05 conditional novelty 7.0 of 10

    Phase-field limits of volume-preserving mean curvature flow satisfy a new Brakke-type inequality and form a volume-preserving Brakke flow globally in time on the torus.

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