Connected sum of manifolds with spectral Ricci lower bounds
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912392108048384 |
|---|---|
| author | Antonelli, Gioacchino Xu, Kai |
| author_facet | Antonelli, Gioacchino Xu, Kai |
| contents | Let $n > 2$, $γ> \frac{n-1}{n-2}$, and $λ\in \mathbb{R}$. We prove that if $M$ and $N$ are two smooth $n$-manifolds that admit a complete Riemannian metric satisfying
\[
-γΔ+ \mathrm{Ric} > λ,
\]
then the connected sum $M \# N$ also admits such a metric. The construction geometrically resembles a Gromov-Lawson tunnel; the range $ γ> \frac{n-1}{n-2} $ is sharp for this to hold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18320 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connected sum of manifolds with spectral Ricci lower bounds Antonelli, Gioacchino Xu, Kai Differential Geometry Analysis of PDEs Let $n > 2$, $γ> \frac{n-1}{n-2}$, and $λ\in \mathbb{R}$. We prove that if $M$ and $N$ are two smooth $n$-manifolds that admit a complete Riemannian metric satisfying \[ -γΔ+ \mathrm{Ric} > λ, \] then the connected sum $M \# N$ also admits such a metric. The construction geometrically resembles a Gromov-Lawson tunnel; the range $ γ> \frac{n-1}{n-2} $ is sharp for this to hold. |
| title | Connected sum of manifolds with spectral Ricci lower bounds |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2505.18320 |