On the derivatives of the Lempert functions

Details On the derivatives of the Lempert functions On the derivatives of the Lempert functions

2008-01-18

arxiv.org/abs/0801.2892v1

Ann. Mat. Pura Appl. 187 (2008), 547-553

Mathematics

Complex Variables

to appear in the Ann. Mat. Pura Appl.

Scientific paper

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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