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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A deformation theorem for the Kobayashi metric


Author: M. Kalka
Journal: Proc. Amer. Math. Soc. 59 (1976), 245-251
MSC: Primary 32H15; Secondary 32G05
MathSciNet review: 0412481
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Abstract: Let $ {M_0}$ be a compact hyperbolic complex manifold. It is shown that the infinitesimal Kobayashi metric is upper semicontinuous in a $ {C^\infty }$ deformation parameter $ t \in U \subseteq {R^k}$. This is accomplished by proving deformation theorems for holomorphic maps.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0412481-4
PII: S 0002-9939(1976)0412481-4
Keywords: Deformation of complex structure, hyperbolic manifold, infinitesimal Kobayashi metric
Article copyright: © Copyright 1976 American Mathematical Society