Regularity of Kobayashi metric
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.
Keywords
Cite
@article{arxiv.1710.09885,
title = {Regularity of Kobayashi metric},
author = {Giorgio Patrizio and Andrea Spiro},
journal= {arXiv preprint arXiv:1710.09885},
year = {2018}
}
Comments
14 pages, 8 figures - The previously announced main result had a gap. In this new version the corrected statement is given. To appear on the volume "Geometric Complex Analysis - Proceedings of KSCV 12 Symposium"