Time: Sunday, August 3rd, 2025,16:15-17:15
Location:IMS, S408
Speaker: Weiyong He, University of Oregon
Abstract: We discuss the uniqueness of well-known open conjecture related to the even logarithm-Minkowski problem and the related even L_p Minkowski problem. We consider the convex bodies in Euclidean space of dimesnion bigger or equal than 3. We prove that there exists a unique p_0 in [0, 1], which can be characterized by the eigenvalue of Hilbert operator related to a convex body, that the even L_p Minkowski problem has a unique solution for p greater or equal than p_0, and uniqueness fails for inifintiely many convex bodies if p is less than p_0. The previous results by many experts in the field asserts that the uniquess holds for p is bigger than p_0.