[Dottorcomp] Seminari di Matematica Applicata, 18/02/2025, Patrick Guidotti

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 18 Febbraio 2025, alle ore 15 precise, presso l'aula Beltrami del
Dipartimento di Matematica,

Patrick Guidotti (University of California at Irvine)
terrà un seminario dal titolo:

The Curve Shortening Flow for Curves of Finite Total Absolute Curvature.

Abstract.
We revisit the well-known Curve Shortening Flow for immersed curves in the
d-dimensional Euclidean space. We exploit a fundamental structure of the
problem to derive a new global construction of a solution, that is, a
construction that is valid for all times and is insensitive to
singularities. The construction is characterized by discretization in time
and the approximant, while still exhibiting the possibile formation of
finitely many singularities at a finite set of singular times, exists
globally. It is also well behaved and simpler to analyze than a solution of
the CSF, which is obtained in the limit. Estimates for a natural
(geometric) norm involving length and total absolute curvature allow
passage to the limit. Many classical qualitative results about the flow can
be recovered by exploiting the simplicity of the approximant and new ones
can be proved. The construction also suggests a numerical procedure for the
computation of the flow which proves very effective as demonstrated by a
series of numerical experiments shown at the end of the talk.

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https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/