Calculus of Variations and Geometric Measure Theory

Topology and geometry of nontrivial rank-one convex hulls

Johannes Zimmer ((MPI Leipzig)

created by alberti on 24 Apr 2004

6 may 2004


Seminari di calcolo delle variazioni

when: Thursday, May 6, at 2.30 and 4 pm

where: Centro De Giorgi

who: Johannes Zimmer (MPI Leipzig)

title: Topology and geometry of nontrivial rank-one convex hulls

abstract: Nonconvex hulls are an important notion in the calculus of variations. In this talk, we will focus on rank-one convex hulls. Specifically, recent results on so-called Tk-configurations as the most prominent case of nontrivial rank-one convex hulls will be reported. We will mainly focus on the most interesting case of 2 by 2 matrices (and explain why this is the most interesting case). We show that T4-configurations are not as exotic objects as one would expect at a first glance, and give a geometric description as well as a characterization of their topological structure in the spaces of quadruples of 2 by 2 matrices. Algorithms for their efficient detection will also be presented. This is joint work with Carl-Friedrich Kreiner, MPI Leipzig.

posted by Giovanni Alberti