Year: 2026
Type: article
Abstract: Let n > 2 n > 2 , γ > n − 1 n − 2 \gamma > \frac {n-1}{n-2} , and λ ∈ R \lambda \in \mathbb {R} . We prove that if M M and N N are two smooth n n -manifolds that admit a complete Riemannian metric satisfying \[ − γ Δ + R i c > λ , -\gamma \Delta + \mathrm {Ric} > \lambda , \] then the connected sum M # N M \# N also admits such a metric. The construction geometrically resembles a Gromov-Lawson tunnel; the range γ > n − 1 n − 2 \gamma > \frac {n-1}{n-2} is sharp for this to hold.
DOI: 10.1090/proc/17633
Authors: Gioacchino Antonelli, Kai Xu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7125367670