Workshop
Nonlocal isoperimetric problems
- Theresa Simon
Abstract
A number of fundamental questions about the structure of matter can be formulated as problems in energy-driven pattern formation. For example, Gamow's liquid drop model addresses the shape and stability properties of atomic nuclei as arising from competition between long-range Coulomb repulsion and short-range attraction modeled by surface tension. This gives rise to a class of variational problems called non-local isoperimetric problems in which surface area minimization is augmented by long-range repulsion. I will discuss the fundamental questions of existence and the shapes of minimizers, including the question of symmetry breaking, in a variety of instances.