A Schwarz lemma for Kähler affine metrics and the canonical potential of a proper convex cone
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| 024 | 7 | 0 | |a 10.1007/s10231-013-0362-6 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-013-0362-6 | ||
| 100 | 1 | |a Fox |D Daniel |u Departamento de Matemática Aplicada, EUIT Industrial, Universidad Politécnica de Madrid, Ronda de Valencia 3, 28012, Madrid, Spain |4 aut | |
| 245 | 1 | 2 | |a A Schwarz lemma for Kähler affine metrics and the canonical potential of a proper convex cone |h [Elektronische Daten] |c [Daniel Fox] |
| 520 | 3 | |a 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 $$n$$ n -dimensional cone, a rescaling of the canonical potential is an $$n$$ 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. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 | ||
| 690 | 7 | |a Convex cones |2 nationallicence | |
| 690 | 7 | |a Kähler affine metrics |2 nationallicence | |
| 690 | 7 | |a Self-concordant barrier |2 nationallicence | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/1(2015-02-01), 1-42 |x 0373-3114 |q 194:1<1 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-013-0362-6 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-013-0362-6 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Fox |D Daniel |u Departamento de Matemática Aplicada, EUIT Industrial, Universidad Politécnica de Madrid, Ronda de Valencia 3, 28012, Madrid, Spain |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/1(2015-02-01), 1-42 |x 0373-3114 |q 194:1<1 |1 2015 |2 194 |o 10231 | ||