Observatorio de I+D+i UPM

Memorias de investigación
Research Publications in journals:
A Schwarz lemma for Kähler affine metrics and the canonical potential of a proper convex cone
Year:2013
Research Areas
  • Differential geometry
Information
Abstract
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.
International
Si
JCR
Si
Title
Annali di Matematica Pura ed Applicata
ISBN
0373-3114
Impact factor JCR
0,909
Impact info
JCR Mathematics 2013. 53 de 299 en matematicas (Q1). 95 de 250 en matematica aplicada (Q2).
Volume
to appear
10.1007/s10231-013-0362-6
Journal number
From page
1
To page
42
Month
SIN MES
Ranking
JCR Mathematics 2013. 53 de 299 en matematicas (Q1). 95 de 250 en matematica aplicada (Q2).
Participants
  • Autor: Daniel Jeremy Fox Hornig (UPM)
Research Group, Departaments and Institutes related
  • Creador: Departamento: Matemática Aplicada (E.U.I.T. Industrial)
S2i 2020 Observatorio de investigación @ UPM con la colaboración del Consejo Social UPM
Cofinanciación del MINECO en el marco del Programa INNCIDE 2011 (OTR-2011-0236)
Cofinanciación del MINECO en el marco del Programa INNPACTO (IPT-020000-2010-22)