Space-time integral currents of bounded variation

Abstract: I will present aspects of a theory of space-time integral currents with bounded variation in time. This is motivated by a recent model for elasto-plastic evolutions that are driven by the flow of dislocations (this model is joint work with T. Hudson). The classical scalar BV-theory can be recovered as the 0-dimensional limit case of this BV space-time theory. However, the emphasis is on evolutions of higher-dimensional objects, most notably 1D loops moving within 3D domains (i.e., the codimension 2 case), which corresponds to dislocation dynamics in a material specimen. Based on this, I will discuss the notion of Lipschitz deformation distance between integral currents, which arises physically as a (simplified) measure of dissipation. In particular, I will explain its relation to the boundaryless Whitney flat metric.

mathematical physicsanalysis of PDEsdifferential geometryfunctional analysis

Audience: researchers in the topic

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.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php