Geometry and Geometric Analysis Working Group

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Elliptic integrands in variational problems.

Speaker: Antonio De Rosa

Location: Warren Weaver Hall 1314

Date: Tuesday, November 5, 2019, 11 a.m.

Synopsis:

Elliptic integrands are used to model anisotropic energies in variational problems. These energies are employed in a variety of applications, such as crystal structures, capillarity problems and gravitational fields, to account for preferred inhomogeneous and directionally dependent configurations. After a brief introduction to variational problems involving elliptic integrands, I will present an overview of the techniques I have developed to prove existence, regularity and uniqueness properties of the critical points of anisotropic energies. In particular, I will present the anisotropic extension of Allard's rectifiability theorem and its applications to the Plateau problem. Furthermore, I will describe the anisotropic counterpart of Alexandrov's characterization of volume-constrained
critical points. Finally, I will mention some of my ongoing and future research projects.