Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows
Annalisa Cesaroni, Lucia De Luca, Matteo Novaga, Marcello Ponsiglione
2021CINECA IRIS Institutial research information system (University of Pisa)12 citationsDOIOpen Access PDF
Abstract
We introduce a notion of uniform convergence for local and nonlocal curvatures. Then, we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation. We apply such a general theory to characterize the limits of s-fractional mean curvature flows as (Formula presented.) and (Formula presented.) In analogy with the s-fractional mean curvature flows, we introduce the notion of s-Riesz curvature flows and characterize its limit as (Formula presented.) Eventually, we discuss the limit behavior as (Formula presented.) of the flow generated by a regularization of the r-Minkowski content.
Topics & Concepts
MathematicsMean curvature flowCurvatureMean curvatureLimit (mathematics)Minkowski spaceMathematical analysisConvergence (economics)Flow (mathematics)Stability (learning theory)GeometryEconomicsEconomic growthMachine learningComputer scienceGeometric Analysis and Curvature FlowsNonlinear Partial Differential EquationsAdvanced Differential Geometry Research