Resolution of singularities of the network flow
Alessandra Pluda (University of Pisa)
Abstract: The curve shortening flow is an evolution equation in which a curve moves with normal velocity equal to its curvature (at any point and time) and can be interpreted as the gradient flow of the length. We consider the same flow for networks (finite unions of sufficiently smooth curves whose end points meet at junctions). Because of the variational nature of the problem, one expects that for almost all the times the evolving network will possess only triple junctions where the unit tangent vectors forms angles of 120 degrees (regular junctions). However, even if the initial network has only regular junctions, this property is not preserved by the flow and junctions of four or more curves may appear during the evolution. The aim of this talk is first to describe the process of singularity formation and then to explain the resolution of such singularities and how to continue the flow in a classical PDE framework.
This is a research in collaboration with Jorge Lira (Universidade Federal do CearĂ¡), Rafe Mazzeo (Stanford University) and Mariel Saez (P. Universidad Catolica de Chile).
analysis of PDEsclassical analysis and ODEsdifferential geometryoptimization and control
Audience: researchers in the topic
( paper )
Online Seminar "Geometric Analysis"
Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.
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Organizers: | Simon Blatt*, Philipp Reiter*, Armin Schikorra*, Guofang Wang |
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