Sharp shifted reciprocal sums of Neumann eigenvalues on space forms

Daguang Chen, Chengxi Yang

Let ${\mathbb{M}}_{\kappa }^n$ be the space form of sectional curvature $\kappa \in \{-1,0,1\}$, so that $\mathbb{M}_{-1}^n=\mathbb{H}^n, \mathbb{M}_{0}^n=\mathbb{R}^n, \mathbb{M}_{1}^n=\mathbb{S}^…