Giammichele Di Matteo (SSM Napoli) – Seminario di Analisi

Martedì, 25 novembre⋅15:00 – 16:00

Title: Higher dimensional Sacks-Uhlenbeck approximation

Abstract: In this talk, we will describe a generalization of Sacks-Uhlenbeck’s existence of harmonic 2-spheres result to higher dimensional domains, that is we construct non-trivial, regular, n-harmonic n-spheres in suitable target manifolds. The proof follows a similar perturbative argument, which in high dimensions leads to a degenerate and double-phase-type Euler-Lagrange system, making the uniform regularity needed to formalise the bubbling harder to achieve. If time permits, we will sketch how to combine these results to solve quite general min-max problems for the n-energy modulo bubbling. This is a joint work with Tobias Lamm.