The space of convex domains in complex Euclidean space

In this mostly expository article, we describe some properties of the space of convex domains in complex Euclidean space (endowed with the local Hausdorff topology). In particular, we give careful proofs that the Kobayashi metric, the Bergman kernel/metric, and the Kähler–Einstein metric are all con...

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Vydáno v:	The Journal of geometric analysis Ročník 30; číslo 2; s. 1312 - 1358
Hlavní autoři:	Gaussier, Hervé, Zimmer, Andrew
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.04.2020 Springer Nature B.V Springer
Témata:	Abstract Harmonic Analysis an Important Tool in Several Complex Variables Automorphisms Closures Convex and Discrete Geometry Differential Geometry Domains Dynamical Systems and Ergodic Theory Euclidean geometry Euclidean space Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Invariant Metrics Mathematics Mathematics and Statistics Topology Invariant metrics and pseudodistances Convex domains 32F17 Primary 32F45
ISSN:	1050-6926, 1559-002X
On-line přístup:	Získat plný text
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Popis
Shrnutí:	In this mostly expository article, we describe some properties of the space of convex domains in complex Euclidean space (endowed with the local Hausdorff topology). In particular, we give careful proofs that the Kobayashi metric, the Bergman kernel/metric, and the Kähler–Einstein metric are all continuous on the space of convex domains. The group of affine automorphisms acts on this space and we also describe the orbit closures for some special classes of domains.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-019-00346-5