Speaker：Qi Guo (Renmin University of China)

Time：2026-10-15 16: 00

Location：Conference Room S207 at Experiment Building at Haiyun Campus

Abstract:

We study harmonic maps from the 2 dimensional unit disk B_1 into S^2 with boundary data given by a once-covered latitude circle. Brézis and Coron constructed two explicit solutions and asked whether there are other solutions. Our main result gives a negative answer: every weak harmonic map with this boundary trace must be one of the two Brézis-Coron maps. The proof uses a boundary rigidity argument based on the Hopf differential, the Pohozaev identity, and the sharp planar isoperimetric inequality.