We review some recent results on existence and regularity of Monge-Ampère 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 on an appropriate 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.

Regularity of Kobayashi Metric

A. Spiro
2018-01-01

Abstract

We review some recent results on existence and regularity of Monge-Ampère 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 on an appropriate 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.
2018
978-981-13-1671-5
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Patrizio G., Spiro A., 2018 - Regularity of Kobayashi Metric. Geometric Complex Analysis, pp. 335–349.pdf

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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11581/422139
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