English

Variational Nonlinear and Nonlocal Curvature Flows

Analysis of PDEs 2025-06-09 v1

Abstract

We prove that the minimizing movements scheme \'a 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.

Keywords

Cite

@article{arxiv.2506.05951,
  title  = {Variational Nonlinear and Nonlocal Curvature Flows},
  author = {Daniele De Gennaro},
  journal= {arXiv preprint arXiv:2506.05951},
  year   = {2025}
}
R2 v1 2026-07-01T03:03:21.506Z