Landau's theorem for holomorphic curves in projective space and the Kobayashi metric on hyperplane complements

Details Landau's theorem for holomorphic curves in projective space and the Kobayashi metric on hyperplane complements Landau's theorem for holomorphic curves in projective space and the Kobayashi metric on hyperplane complements

2006-07-28

arxiv.org/abs/math/0607743v2

Pure Appl. Math. Q. 7 (2011), 199-221

Mathematics

Complex Variables

18 pages, 2 figures, Theorem 4.2 improved in this version. To appear in Pure and Applied Mathematics Quarterly

Scientific paper

We prove an effective version of a theorem of Dufresnoy: For any set of 2n+1 hyperplanes in general position in n-dimensional complex projective space, we find an explicit constant K such that for every holomorphic map f from the unit disc to the complement of these hyperplanes, the derivative of f at the origin measured with respect to the Fubuni-Study metric is bouned above by K. This result gives an explicit lower bound on the Royden function, i.e., the ratio of the Kobayashi metric on the hyperplane complement to the Fubini-Study metric. Our estimate is based on the potential-theoretic method of Eremenko and Sodin.

Affiliated with

Also associated with

No associations

Rating

Landau's theorem for holomorphic curves in projective space and the Kobayashi metric on hyperplane complements does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Landau's theorem for holomorphic curves in projective space and the Kobayashi metric on hyperplane complements, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Landau's theorem for holomorphic curves in projective space and the Kobayashi metric on hyperplane complements will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-251379