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arXiv · 2505.18320

Connected sum of manifolds with spectral Ricci lower bounds

Gioacchino Antonelli·Kai Xu
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Abstract

Let $n > 2$, $\gamma > \frac{n-1}{n-2}$, and $\lambda \in \mathbb{R}$. We prove that if $M$ and $N$ are two smooth $n$-manifolds that admit a complete Riemannian metric satisfying \[-\gamma\Delta + \mathrm{Ric} > \lambda,\]then the connected sum $M \# N$ also admits such a metric. The construction geometrically resembles a Gromov-Lawson tunnel; the range $ \gamma > \frac{n-1}{n-2} $ is sharp for this to hold.

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Gioacchino Antonelli, Kai Xu. 2025-05-23. Connected sum of manifolds with spectral Ricci lower bounds. https://arxiv.org/abs/2505.18320

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