Evolution of networks with multiple junctions
Carlo Mantegazza, Matteo Novaga, Alessandra Pluda, Felix Schulze
TL;DR
This paper studies the evolution of planar networks of curves driven by curvature, focusing on their existence, uniqueness, singularities, and long-term behavior.
Contribution
It provides new insights into the mathematical properties and evolution dynamics of networks with multiple junctions under curvature flow.
Findings
Existence and uniqueness results for the flow.
Characterization of singularity formation.
Analysis of asymptotic behavior of networks.
Abstract
We consider the motion by curvature of a network of curves in the plane and we discuss existence, uniqueness, singularity formation and asymptotic behavior of the flow.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Mathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows