English

Weakly holomorphic homogeneous regular manifolds

Complex Variables 2025-03-25 v1 Differential Geometry

Abstract

We introduce a class of complex manifolds which we call weakly holomorphic homogeneous regular manifolds (wHHR) manifolds. As the name suggests, this class contains the so-called holomorphic homogeneous regular manifolds but also other classes of complex manifolds such as two dimensional finite type domains and simply connected K\"ahler manifolds with pinched negative sectional curvature. For wHHR Stein manifolds we prove that the Bergman and Kobayashi metrics are biLipschitz equivalent.

Keywords

Cite

@article{arxiv.2503.17848,
  title  = {Weakly holomorphic homogeneous regular manifolds},
  author = {Andrew Zimmer},
  journal= {arXiv preprint arXiv:2503.17848},
  year   = {2025}
}

Comments

v1: 26 pages. Comments welcome!

R2 v1 2026-06-28T22:31:00.726Z