A Schwarz lemma for Kahler affine metrics and the canonical potential of a proper convex cone
Data(s) |
01/02/2015
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Resumo |
This is an account of some aspects of the geometry of Kahler affine metrics based on considering them as smooth metric measure spaces and applying the comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a version for Kahler affine metrics of Yau s Schwarz lemma for volume forms. By a theorem of Cheng and Yau, there is a canonical Kahler affine Einstein metric on a proper convex domain, and the Schwarz lemma gives a direct proof of its uniqueness up to homothety. The potential for this metric is a function canonically associated to the cone, characterized by the property that its level sets are hyperbolic affine spheres foliating the cone. It is shown that for an n -dimensional cone, a rescaling of the canonical potential is an n -normal barrier function in the sense of interior point methods for conic programming. It is explained also how to construct from the canonical potential Monge-Ampère metrics of both Riemannian and Lorentzian signatures, and a mean curvature zero conical Lagrangian submanifold of the flat para-Kahler space. |
Formato |
application/pdf |
Identificador | |
Idioma(s) |
eng |
Publicador |
E.U.I.T. Industrial (UPM) |
Relação |
http://oa.upm.es/33432/1/INVE_MEM_2013_144009.pdf http://link.springer.com/article/10.1007%2Fs10231-013-0362-6 info:eu-repo/semantics/altIdentifier/doi/10.1007/s10231-013-0362-6 |
Direitos |
http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/restrictedAccess |
Fonte |
Annali di Matematica Pura ed Applicata, ISSN 0373-3114, 2015-02-01, Vol. 194, No. 1 |
Palavras-Chave | #Matemáticas |
Tipo |
info:eu-repo/semantics/article Artículo PeerReviewed |