Convexity and Teichmüller spaces

Convexity and Teichmüller spaces

We provide a negative answer to Royden’s problem whether any finite dimensional Teichmüller space of dimension greater than 1 is biholomorhically equivalent to a bounded convex domain in complex Euclidean space. We prove that any Teichmüller space T (0, n ) of punctured spheres with a sufficiently l...

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Veröffentlicht in:Lobachevskii journal of mathematics 2017-03, Vol.38 (2), p.307-314
1. Verfasser: Krushkal, S. L.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Convexity
Euclidean geometry
Euclidean space
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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Zusammenfassung:We provide a negative answer to Royden’s problem whether any finite dimensional Teichmüller space of dimension greater than 1 is biholomorhically equivalent to a bounded convex domain in complex Euclidean space. We prove that any Teichmüller space T (0, n ) of punctured spheres with a sufficiently large number n ≥ n 0 > 4 of punctures cannot be mapped biholomorphically onto a bounded convex domain in ℂ n −3 .
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080217020135