zur Startseite

Enno Lenzmann

Spectral problems for half-harmonic maps

Abstract: Half-harmonic maps are intriguing objects with close connections to minimal surfaces, conformal geometry, and completely integrable systems. In my talk, I will focus on the the so-called energy-critical case of half-harmonic maps from the real line (R) to the two-dimensional unit sphere (S^2). In particular, I will discuss spectral key properties of the linearized operator around such half-harmonic maps. A striking feature of these (nonlocal) operators is that they can be analyzed in great detail by looking at certain Jacobi-type operators acting on the unit circle. This is joint work with Armin Schikorra (Freiburg i. Br.).