Title: Sharp shifted reciprocal sums of Neumann eigenvalues on space forms
Speaker: Daguang Chen (Tsinghua University)
Time: 8.5(Wednesday), 11:00-12:00
Venue: Mingde Building B201-1
Abstract: We study sharp lower bounds for shifted reciprocal sums of Neumann eigenvalues on bounded domains in Euclidean, hyperbolic, and spherical spaces. Motivated by the classical Szegő–Weinberger inequality, the Ashbaugh–Benguria reciprocal conjecture, and the two-ball problem, we prove
Equality holds precisely when (\Omega) is the disjoint union of two equal geodesic balls. This confirms the Bucur–Martinet–Nahon conjecture on the sphere and establishes its Euclidean and hyperbolic counterparts. The proof combines folding and centering, two-layer mass transplantation, a shifted Ritz principle, and a trace-free matrix inequality. In this talk, I will describe the historical background, state the main result, and explain the ideas of the proof. This is joint work with Chengxi Yang.
