On the derivatives of the Lempert functions

Nikolai Nikolov; Peter Pflug

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arXiv · 0801.2892

On the derivatives of the Lempert functions

Nikolai Nikolov·Peter Pflug

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Abstract

We show that if the Kobayashi--Royden metric of a complex manifold is continuous and positive at a given point and any non-zero tangent vector, then the "derivatives" of the higher order Lempert functions exist and equal the respective Kobayashi metrics at the point. It is a generalization of a result by M. Kobayashi for taut manifolds.

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Nikolai Nikolov, Peter Pflug. 2008-01-18. On the derivatives of the Lempert functions. https://arxiv.org/abs/0801.2892

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