Speaker：Bin Deng (Wuhan University)

Time：2026-10-16 10: 00

Location：Conference Room S207 at Experiment Building at Haiyun Campus

Abstract:

The Nitsche problem is a classical problem in harmonic mapping theory concerning the existence of harmonic homeomorphisms between annuli and the optimal geometric conditions for such mappings. While the planar case is well understood, its higher-dimensional extension presents substantial new difficulties.In this talk, I will present sharp geometric bounds and rigidity results for harmonic homeomorphisms between concentric spherical annuli in higher dimensions. The results also extend to more general harmonic maps with nonzero topological degree. The main approach combines Poisson representations, topological information, and a new boundary coupling mechanism to reduce the problem to sharp integral estimates. Possible applications to other extremal problems for mappings between annuli will also be discussed. This is a joint work with Jiahuan Li, Yilu Liu and Xi-nan Ma.