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arXiv · 2506.05951

Variational Nonlinear and Nonlocal Curvature Flows

Daniele De Gennaro
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Abstract

We prove that the minimizing movements scheme á la Almgren-Taylor-Wang converges towards level-set solutions to a nonlinear version of nonlocal curvature flows with time-depending forcing term, in the rather general framework of variational curvatures introduced in \cite{ChaMorPon15}. The nonlinearity involved is assumed to satisfy minimal assumptions, namely continuity, monotonicity, and vanishing at zero. Under additional assumptions only on the curvatures involved, we establish uniqueness for level-set solutions.

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Daniele De Gennaro. 2025-06-06. Variational Nonlinear and Nonlocal Curvature Flows. https://arxiv.org/abs/2506.05951

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