Year: 2026
Type: preprint
Abstract: Let $(M^{n+1},g)$ be a compact Riemannian manifold with boundary. Under the assumptions $\Ric_g\geq ng$ and $\II_g\geq0$, Wang proposed a sharp strengthening of the Choi--Wang--Reilly estimate, asserting that the first nonzero Laplace eigenvalue of the boundary is at least $n$; see [J. Geom. Anal. 31 (2021)]. We disprove this assertion in every dimension $n+1\geq3$. More precisely, we construct a sequence of metrics on the hemisphere $\Sph^{n+1}_{+}$ converging in $C^\infty$ to the round metric and satisfying \[ \Ric_g>n g,\qquad \II_g>0,\qquad λ_1(\partial\Sph^{n+1}_{+},g|_{\partial\Sph^{n+1}_{+}})
Source: arXiv (Cornell University)
Authors: Li, Fagui, Zhao, Yuhang
Institutions: Beijing Institute of Technology, Nanjing University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204435088