Seminar| Institute of Mathematical Sciences
Time: Thursday, October 22th, 2026,16:00-17:00
Location: IMS S408
Speaker: Siran Li, Shanghai Jiaotong University
Abstract:We prove that for every dimension n≥2 and parameter p∈]1,n[, the hedgehog u0(x)=x/|x| is the unique minimiser of the p-energy in the class of W^{1,p}-mappings from the n-dimensional unit ball to the (n−1)-dimensional unit sphere whose trace equal to the identity on the sphere. This answers in the affirmative an open question on p.29 in [Robert M. Hardt, Singularities of harmonic maps, Bull. Amer. Math. Soc. (N.S.) 34 (1997), 15--34]. The proof exploits ideas from geometric measure theory and, somewhat surprisingly, statistics.