The Weyl functional near the Yamabe invariant
| dc.creator | Akutagawa, Kazuo | |
| dc.creator | Botvinnik, Boris | |
| dc.creator | Kobayashi, Osamu | |
| dc.creator | Seshadri, Harish | |
| dc.date | 2002-01-16 | |
| dc.date | 2002-02-05 | |
| dc.date.accessioned | 2026-07-07T04:45:55Z | |
| dc.date.available | 2026-07-07T04:45:55Z | |
| dc.description | For a compact manifold $M$ of $\dim M =n\geq 4$, we study two conformal invariants of a conformal class $C$ on $M$. These are the Yamabe constant $Y_C(M)$ and the $L^{\frac{n}{2}}$-norm $W_C(M)$ of the Weyl curvature. We prove that for any manifold $M$ there exists a conformal class $C$ such that the Yamabe constant $Y_C(M)$ is arbitrarily close to the Yamabe invariant $Y(M)$, and, at the same time, the constant $W_C(M)$ is arbitrarily large. We study the image of the map $\YW: C\mapsto (Y_C(M),W_C(M))\in \R^2$ near the line $\{(Y(M),w) | w\in \R\}$. We also apply our results to certain classes of 4-manifolds, in particular, minimal compact Kähler surfaces of Kodaira dimension 0, 1 or 2. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0201153 | |
| dc.identifier | http://arxiv.org/abs/math/0201153 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63132 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | Algebraic Topology | |
| dc.subject | Geometric Topology | |
| dc.subject | 53C20 | |
| dc.title | The Weyl functional near the Yamabe invariant | |
| dc.type | text |