The Weyl functional near the Yamabe invariant

dc.creatorAkutagawa, Kazuo
dc.creatorBotvinnik, Boris
dc.creatorKobayashi, Osamu
dc.creatorSeshadri, Harish
dc.date2002-01-16
dc.date2002-02-05
dc.date.accessioned2026-07-07T04:45:55Z
dc.date.available2026-07-07T04:45:55Z
dc.descriptionFor 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.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0201153
dc.identifierhttp://arxiv.org/abs/math/0201153
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63132
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subjectAlgebraic Topology
dc.subjectGeometric Topology
dc.subject53C20
dc.titleThe Weyl functional near the Yamabe invariant
dc.typetext

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