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Seminario di Equazioni Differenziali e Applicazioni: “Parametrized stationary varifolds in two dimensions: regularity and applications”

Giovedì 26 Aprile 2018, ore 12:30 12:00 - Aula 2BC30 Sala Riunioni VII Piano - Alessandro Pigati

ARGOMENTI: Seminari

Giovedì 26 Aprile 2018 alle ore 12:30 12:00 in Aula 2BC30 Sala Riunioni VII Piano, Alessandro Pigati (ETH, Zurigo) terrà un seminario dal titolo “Parametrized stationary varifolds in two dimensions: regularity and applications”.

Abstract
Currents and varifolds are a weak notion of submanifold, designed to build a coordinate-free calculus of variations for the area functional. Varifolds are useful especially when dealing with min-maxes. After a brief historical introduction, we will explore a new notion of “two-dimensional parametrized stationary varifold”, which mixes the classical parametrized approach with the modern varifold approach. In contrast with the lack of regularity for general integer stationary varifolds, we will see how the interaction between the parametrized structure and the stationarity allows to get an optimal regularity result, independent of the codimension. We will also look at a couple of applications: namely, an existence result for immersed minimal surfaces and a nontrivial fact about the conductivity equation.
This is joint work with Tristan Riviere.

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