Elliptic integrands in geometric variational problems

Job Candidate Talk
Thursday, January 9, 2020 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Antonio De Rosa – NYU – derosa@cims.nyu.eduhttps://sites.google.com/view/antonioderosa
Andrzej Swiech

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.