Geometry Seminar: G. Di Matteo (KIT)
Geometry Seminar (Geometric Analysis)
Speaker: Gianmichele Di Matteo (KIT)
Title: Higher dimensional Sacks-Uhlenbeck approximation
Speaker: Gianmichele Di Matteo (KIT)
Title: Higher dimensional Sacks-Uhlenbeck approximation
Abstract:In this talk, we will introduce 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. Then, we develop a refined neck-analysis leading to a quantization of the energy along the approximation, assuming a suitable Struwe-type entropy bound along a sequence of critical points. Finally, we combine these results to solve quite general min-max problems for the n-energy modulo bubbling.