Invariant metrics of model domains near pseudoconcave points

TL;DR

This paper provides detailed estimates of holomorphically invariant metrics near pseudoconcave points in model domains in complex two-space, extending previous results to more general defining functions.

Contribution

It introduces precise metric estimates near pseudoconcave points for a broad class of model domains, generalizing earlier work to include more complex defining functions.

Findings

Extended metric estimates to more general defining functions.

Provided precise bounds for invariant metrics near pseudoconcave points.

Built upon and generalized previous results in complex analysis.

Abstract

We give precise estimates of some holomorphically invariant infinitesimal metrics near a pseudoconcave points in a wide family of ``model'' domains for that situation in $\mathbb C^2$. This extends to metrics (rather distances) the authors' previous results from arXiv:2503.19754 and also takes into account defining functions more general than just power functions.