On Yamabe constants of Riemannian products
| dc.creator | Akutagawa, Kazuo | |
| dc.creator | Florit, Luis A. | |
| dc.creator | Petean, Jimmy | |
| dc.date | 2006-03-20 | |
| dc.date.accessioned | 2026-07-07T07:07:06Z | |
| dc.date.available | 2026-07-07T07:07:06Z | |
| dc.description | For a closed Riemannian manifold $(M^m,g)$ of constant positive scalar curvature and any other closed Riemannian manifold $(N^n,h)$, we show that the limit of the Yamabe constants of the Riemannian products $(M\times N,g+rh)$ as $r$ goes to infinity is equal to the Yamabe constant of $(M^m \times R^n, [g+g_E])$ and is strictly less than the Yamabe invariant of $S^{m+n}$ provided $n\geq 2$. We then consider the minimum of the Yamabe functional restricted to functions of the second variable and we compute the limit in terms of the best constants of the Gagliardo-Nirenberg inequalities. | |
| dc.description | 17 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0603486 | |
| dc.identifier | http://arxiv.org/abs/math/0603486 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110267 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C21 | |
| dc.title | On Yamabe constants of Riemannian products | |
| dc.type | text |