Regularity of Kobayashi metric
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Publication:1625409
DOI10.1007/978-981-13-1672-2_24zbMATH Open1410.32016arXiv1710.09885OpenAlexW3101543462MaRDI QIDQ1625409
Giorgio Patrizio, Andrea F. Spiro
Publication date: 29 November 2018
Abstract: We review some recent results on existence and regularity of Monge-Amp`ere exhaustions on the smoothly bounded strongly pseudoconvex domains, which admit at least one such exhaustion of sufficiently high regularity. A main consequence of our results is the fact that the Kobayashi pseudo-metric k on an appropriare open subset of each of the above domains is actually a smooth Finsler metric. The class of domains to which our result apply is very large. It includes for instance all smoothly bounded strongly pseudoconvex complete circular domains and all their sufficiently small deformations.
Full work available at URL: https://arxiv.org/abs/1710.09885
Kobayashi metricdeformations of complex structuresMonge-Ampère equationsmanifolds of circular typepluricomplex Green functions
Hyperbolic and Kobayashi hyperbolic manifolds (32Q45) Deformations of complex structures (32G05) Complex Monge-Ampère operators (32W20)
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