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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Analysis of the Wu metric II: The case of non-convex Thullen domains
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by C. K. Cheung and K. T. Kim
Proc. Amer. Math. Soc. 125 (1997), 1131-1142
DOI: https://doi.org/10.1090/S0002-9939-97-03695-2

Abstract:

We present an explicit description of the Wu invariant metric on the non-convex Thullen domains. We show that the Wu invariant Hermitian metric, which in general behaves as nicely as the Kobayashi metric under holomorphic mappings, enjoys better regularity in this case. Furthermore, we show that the holomorphic curvature of the Wu metric is bounded from above everywhere by $-1/2$. This leads the Wu metric to be a natural solution to a conjecture of Kobayashi in the case of non-convex Thullen domains.
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Bibliographic Information
  • C. K. Cheung
  • Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02167
  • Email: Cheung/MT@hermes.bc.edu
  • K. T. Kim
  • Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784 Republic of Korea
  • Email: kimkt@posmath.postech.ac.kr
  • Received by editor(s): October 11, 1995
  • Additional Notes: Research of the second named author is supported in part by Grants from Pohang University of Science and Technology (POSTECH), GARC, and BSRI
  • Communicated by: Peter Li
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 1131-1142
  • MSC (1991): Primary 32H15
  • DOI: https://doi.org/10.1090/S0002-9939-97-03695-2
  • MathSciNet review: 1363414