Calculus of Variations and Geometric Measure Theory
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Topological singularities of vector-valued maps

Giacomo Canevari (Dip. Informatica, Università degli Studi di Verona)

created by gelli on 08 Feb 2021
modified on 17 Feb 2021

17 feb 2021 -- 17:00   [open in google calendar]

Dipartimento di Matematica di Pisa online

Abstract.

Let N be a smooth, compact, connected submanifold of a Euclidean space. We are interested in vector-valued Sobolev maps u that take their values 'close' to the manifold N - and the 'closeness' is measured, e.g., in an integral sense. For instance, u may be a Sobolev approximation of an N-valued map with singularities. Our goal is to define the `set of topological singularities' of such a map u. In some cases, this task can be accomplished by considering the distributional Jacobian of u. In this talk, instead, we will describe a different approach, based on flat chains. As an application, we will state a Gamma-convergence result for generalised Ginzburg-Landau functionals. The talk is based on a joint work with Giandomenico Orlandi (Verona).

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