Perelman's λfunctional and the Seiberg-Witten equations

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dc.creatorFang, Fuquan
dc.creatorZhang, Yuguang
dc.date2006-08-17
dc.date.accessioned2026-07-07T07:21:53Z
dc.date.available2026-07-07T07:21:53Z
dc.descriptionIn this paper we study the supremum of Perelman's λ-functional {λ}_M(g) on Riemannian 4-manifold M by using the Seiberg-Witten equations. We prove among others that, for a compact Kähler-Einstein complex surface (M, J, g_{0}) with negative scalar curvature, (i) If g_{1} is a Riemannian metric on M with λ_{M}(g_{1})= λ_{M}(g_{0}), then Vol_{g_{1}}(M)\geq Vol_{g_{0}}(M). Moreover, the equality holds if and only if g_{1} is also a Kähler-Einstein metric with negative scalar curvature. (ii) If g_{t}, t\in [-1,1], is a family of Einstein metrics on M with initial metric g_{0}, then g_{t} is a Kähler-Einstein metric with negative scalar curvature.
dc.identifierhttps://arxiv.org/abs/math/0608439
dc.identifierhttp://arxiv.org/abs/math/0608439
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115460
dc.subjectFunctional Analysis
dc.subjectGeometric Topology
dc.titlePerelman's λfunctional and the Seiberg-Witten equations
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