A diffusion driven curvature flow

2016/03/03 by Emre Baspinar, Baspinar, Emre, Giovanna Citti +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Biology Tumor Growth #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1603.01156

openalex publication_date 2016/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Bence-Merriman-Osher algorithm computes numerically mean curvature flow via solutions of heat equation iteratively initialized at the end of each short time interval. Inspired by the convergence proof of Evans of this algorithm where he employed nonlinear semigroup theory and level set approach to mean curvature flow, we prove here that a similar procedure, but now with a different definition of evolved surface at the end of each short time interval, results in a motion by curvature. The interest of this version of the algorithm is its application corresponding to model of the visual cortex.

Citations

• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations

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