communication: Elastic energy for networks
speaker: Alessandra Pluda (Università di Pisa)abstract: A network $\Gamma$ is a finite union of curves $\gammai$ whose end points meet in junctions.
We consider the elastic energy functional for $\Gamma$ defined as
$E(\Gamma):=\int{\Gamma} k2\,{\rm{d}}s=\sum{i}\int{\gammai}\left(ki\right)2\,{\rm{d}}si$,
where $ki$ and $si$ denote the scalar curvature and the arc—length parameter of $\gammai$, respectively.
Fixed a certain class of networks (namely fixed the number of curves and number of junctions), we want to:
(1) study the minimization of E among all networks in the given class; (2) study the solutions of the $L2$ gradient flow of the energy E with a network in the given class as initial datum.
Aim of the talk is the explanation of these two problems getting into details in the simplest case of one single curve.
timetable:
Thu 30 Aug, 17:45 - 18:25, Sala Riunioni del Centro De Giorgi
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