Relative $K$-stability and modified $K$-energy on toric manifolds

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dc.creatorZhou, Bin
dc.creatorZhu, Xiaohua
dc.date2006-03-09
dc.date.accessioned2026-07-07T07:06:44Z
dc.date.available2026-07-07T07:06:44Z
dc.descriptionIn this paper, we discuss the relative $K$-stability and the modified $K$-energy associated to the Calabi's extremal metric on toric manifolds. We give a sufficient condition in the sense of convex polytopes associated to toric manifolds for both the relative $K$-stability and the properness of modified $K$-energy. In particular, our results hold for toric Fano manifolds with vanishing Futaki-invariant. We also verify our results on the toric Fano surfaces.
dc.identifierhttps://arxiv.org/abs/math/0603237
dc.identifierhttp://arxiv.org/abs/math/0603237
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110137
dc.subjectDifferential Geometry
dc.subject32J15, 53C55, 58E11
dc.titleRelative $K$-stability and modified $K$-energy on toric manifolds
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