Zywomir Dinew
On the Bergman Representative Coordinates
Preprint series: ESI preprints

MSC:

32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA) in $n$ dimensions), See also {46Exx}

32H10 Bergman kernel function, representative domains

32H02 Holomorphic mappings, (holomorphic) embeddings and related questions

32A10 Holomorphic functions

32H15 Invariant metrics and pseudodistances

32C17 Kahler geometry, {For differential-geometric methods, See

Abstract: We study the set where the so-called Bergman representative coordinates
(or Bergman functions) form an immersion. We provide an estimate of the
size of a maximal geodesic ball with respect to the Bergman metric,
contained in this set. By concrete examples we show that these
estimates are the best possible.


Keywords: representative coordinates, Bergman metric, geodesic ball, Lu Qi-keng conjecture, Hermitian geometry