Partial regularity for fractional harmonic maps into spheres

Abstract: Similarly to “classical” harmonic maps, which are critical points of the Dirichlet energy, fractional harmonic maps are defined as critical points of a fractional Dirichlet energy associated with the $s$-power of the Laplacian, for $s \in (0,1)$. In this talk, after a brief reminder on classical harmonic maps, I will present the fractional setting and the partial regularity results we have obtained for maps valued into a sphere. In the case of half harmonic maps ($s=\frac{1}{2}$), I will also recall the connection with minimal surfaces with free boundary, which allowed us to improve known regularity results for energy minimizing maps into spheres.

Mathematics

Audience: researchers in the topic

( paper )

---

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php

---