Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.19807

Finite volume quotients of bounded domains with piecewise smooth boundary

Xingsi Pu·Lang Wang
View original source ↗Read source document ↗Export metadata ↓

Abstract

We prove that a bounded pseudoconvex domain with piecewise $C^2$-smooth boundary which has a finite volume quotient for the complete Kähler-Einstein metric is biholomorphic to a product of complex unit balls. More generally, the same conclusion holds for a bounded domain possessing a boundary point satisfying Kodama's conditions (C.1)-(C.5), provided the quotient has finite volume for a complete $\operatorname{Aut}(D)$-invariant Kähler metric. For piecewise Levi-flat boundary the product is a polydisk and in the smooth pseudoconvex case it is a single ball.

Explore related subjects

math.CV

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Xingsi Pu, Lang Wang. 2026-10-14. Finite volume quotients of bounded domains with piecewise smooth boundary. https://arxiv.org/abs/2610.19807

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Corona Problem for Slice Holomorphic Functions via the Matrix Corona Problem

In this paper we prove the Corona theorem for slice hyperholomorphic functions in a general way that applies to functions with values in a Clifford algebra $\mathbb R_n$ for any $n\geq 2$. This general proof is based on a matrix version of Corona's theorem and then exploiting some symmetries of the matrices that allow to reconstruct the values of the functions. The crucial idea is to tie together the algebra of the functions, the Bezout identities and the Carleson-type conditions. The results we obtain rest on a new way of writing the slice product which improves the standard approach and which holds in general dimension.

math.CV↗
arXiv2026

Transverse analytic envelopes and integrability

We associate normal toric transverse analytic envelopes with the singular orbits of diagonal holomorphic actions, and construct their canonical flat transport. At independent singular supports, the semiglobal first-integral algebra is determined by periodic resonances; complete integrability is equivalent to full resonance rank and finite envelope monodromy. We classify labelled residual actions with a fixed envelope by Grassmannian families and reconstruct the ambient weights from the labelled quotient and logarithmic residues at full resonance rank. For commuting vector fields in convergent simultaneous semisimple normal form, we identify the algebra of holomorphic first integrals with the common kernel of the derivations induced on the toric envelope. Under compatible flat transport this yields a semiglobal criterion. Polynomial examples show that losses of first integrals may be invisible to any prescribed finite jet.

math.CV↗
arXiv2026

Optimal Linear Dependence on Boundary Type for Local Gromov Hyperbolicity of the Kobayashi Metric

The Gromov hyperbolicity constant of a metric space \((X,d)\) is the infimum of all \(δ\ge0\) such that \((X,d)\) is \(δ\)-hyperbolic. For a Kobayashi hyperbolic domain \(Ω\subset\C^n\) and a boundary point \(p\in\partialΩ\), let \(δ_{\mathrm{loc}}(Ω,p)\) denote the local Gromov hyperbolicity constant obtained by restricting the points to arbitrarily small Euclidean neighborhoods of \(p\), while distances are still measured by the ambient Kobayashi distance \(K_Ω\). For each even integer \(M\ge2\), let \(\mathfrak H(M)\) be the supremum of these constants over all complex dimensions \(n\ge2\) and all domains whose boundary is smooth and convex near the distinguished point and has D'Angelo type at most \(M\) at that point. We prove \[ \frac{\log 2}{2} M \le \mathfrak H(M) < 36M. \] Thus the optimal universal dependence of the local Gromov hyperbolicity constant on boundary type is linear. We also show that no analogous bound holds for the global Gromov hyperbolicity constant, even among smooth bounded strongly convex domains.

math.CV↗