Avoidance for set-theoretic solutions of mean-curvature-type flows
Or Hershkovits, Brian White
Abstract
We provide a self-contained treatment of set-theoretic subsolutions to flow by mean curvature, or, more generally, to flow by mean curvature plus an ambient vector field. The ambient space can be any smooth Riemannian manifold. Most importantly, we show that if two such set-theoretic subsolutions are initially disjoint, then they remain disjoint as long as one of the subsolutions is compact; previously, this was only known for Euclidean space (with no ambient vectorfield). The new version (March 2020) incorporates improvements suggested by the CAG referee.
Topics & Concepts
MathematicsDisjoint setsAmbient spaceCurvatureEuclidean spaceMean curvature flowSpace (punctuation)Manifold (fluid mechanics)Set (abstract data type)Pure mathematicsFlow (mathematics)Type (biology)Vector fieldMean curvatureCombinatoricsGeometryComputer scienceGeologyMechanical engineeringEngineeringProgramming languageOperating systemPaleontologyGeometric Analysis and Curvature FlowsTopological and Geometric Data AnalysisMathematical Dynamics and Fractals