Some new domains with complete Kähler metrics of negative curvature

Cheung, Chi-Keung; Wu, Hung-Hsi

doi:10.1007/bf02921334

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1995

1997

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“…So far, most known examples of bounded domains that admit negatively curved complete metrics are convex or essentially convex ( [2], [3], [9], [10], [14], [15] to cite only a few). Note that the domain E λ , 0 < λ < 1/2, cannot be biholomorphically mapped onto any bounded convex domain in C 2 , since its Kobayashi indicatrix is not convex ( [18]).…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Wu metric II: The case of non-convex Thullen domains

Cheung

Kim

1997

Proc. Amer. Math. Soc.

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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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