Local and non-local minimal surfaces

  • Alessio Figalli (The University of Texas at Austin)
G3 10 (Lecture hall)


Nonlocal minimal surfaces naturally appear when studying the structure of interphases that arise in classical phase field models with very long space correlations. These surfaces are boundaries of sets whose characteristic functions minimize a fractional Sobolev norm, and they generalize the classical notion of minimal surfaces in geometric measure theory. In this talk we’ll explain and compare the general regularity theory for both local and non-local minimal surfaces, and discuss several recent developments and open problems.

Katja Heid

Bernd Kirchheim

Universität Leipzig

Stephan Luckhaus

Universität Leipzig

Emanuele Spadaro

Max-Planck-Institut für Mathematik in den Naturwissenschaften