Open Access
1992 The Kobayashi metric of a complex ellipsoid in {${\bf C}\sp 2$}
Brian E. Blank, Da Shan Fan, David Klein, Steven G. Krantz, Daowei Ma, Myung-Yull Pang
Experiment. Math. 1(1): 47-55 (1992).


The infinitesimal Kobayashi metric of an ellipsoid of the form $$ E_m=\{(z_1,z_2)\in \C^2:|z_1|^2+|z_2|^{2m}<1\} $$ is calculated explicitly, modulo a parameter that is determined by solving a transcendental equation. Using this result, we show that the metric is $C^1$ on the tangent bundle away from the zero section. We also describe software that will calculate, using a Monte Carlo method, the infinitesimal Kobayashi metric on a domain of the form $$ \Omega_\rho=\{(z_1,z_2)\in\C^2:\rho(z_1,z_2)<0\}, $$ where $\rho$ is a real-valued polynomial. We compare results of computer calculations with those obtained from the explicit formula for the Kobayashi metric.


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Brian E. Blank. Da Shan Fan. David Klein. Steven G. Krantz. Daowei Ma. Myung-Yull Pang. "The Kobayashi metric of a complex ellipsoid in {${\bf C}\sp 2$}." Experiment. Math. 1 (1) 47 - 55, 1992.


Published: 1992
First available in Project Euclid: 26 March 2003

zbMATH: 0783.32012
MathSciNet: MR93H:32032

Primary: 32H15

Rights: Copyright © 1992 A K Peters, Ltd.

Vol.1 • No. 1 • 1992
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