Memorias de investigación
Artículos en revistas:
A Schwarz lemma for Kähler affine metrics and the canonical potential of a proper convex cone
Año:2013
Áreas de investigación
  • Geometría diferencial
Datos
Descripción
This is an account of some aspects of the geometry of Kähler 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 Kähler affine metrics of Yau's Schwarz lemma for volume forms. By a theorem of Cheng and Yau, there is a canonical Kähler 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-Kähler space.
Internacional
Si
JCR del ISI
Si
Título de la revista
Annali di Matematica Pura ed Applicata
ISSN
0373-3114
Factor de impacto JCR
0,909
Información de impacto
JCR Mathematics 2013. 53 de 299 en matematicas (Q1). 95 de 250 en matematica aplicada (Q2).
Volumen
to appear
DOI
10.1007/s10231-013-0362-6
Número de revista
Desde la página
1
Hasta la página
42
Mes
SIN MES
Ranking
JCR Mathematics 2013. 53 de 299 en matematicas (Q1). 95 de 250 en matematica aplicada (Q2).
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Participantes
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  • Creador: Departamento: Matemática Aplicada (E.U.I.T. Industrial)