Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2611.07098

Non-Kähler Hyperbolicity: Surfaces and Codimension One

Samir Marouani
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study hyperbolicity notions for compact complex manifolds defined by special Hermitian metrics and by holomorphic maps from $\mathbb C^{n-1}$ (divisorial hyperbolicity). For surfaces we show that divisorial and Brody hyperbolicity coincide and that Hermitian-symplectic and Kähler hyperbolicity coincide when $h^{2,0}=0$. In any dimension we prove obstructions to Gauduchon hyperbolicity, show that projective spaces are not divisorially hyperbolic, and give divisorially hyperbolic manifolds that are not balanced hyperbolic.

Explore related subjects

math.CV

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Samir Marouani. 2026-11-04. Non-Kähler Hyperbolicity: Surfaces and Codimension One. https://arxiv.org/abs/2611.07098

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

KEEP EXPLORING

Related papers

arXiv2026

Log canonical singularities of plurisubharmonic functions

A plurisubharmonic weight is \emph{log canonical} if it is at the critical point of turning non-integrable. Given a log canonical plurisubharmonic weight, we show that locally there always exists a log canonical `holomorphic' weight having the same non-integrable locus. The proof uses the theory of quasimonomial valuations developed by Jonsson-Mustaţă and Xu, as well as the minimal model program over complex analytic spaces due to Fujino and Lyu-Murayama. As a consequence, we obtain that the non-integrable locus is seminormal.

math.CV↗
arXiv2026

Sobolev homeomorphisms and Jordan curves with positive area

Each homeomorphic parametrization of a Jordan curve via the unit circle $\mathbb{S}\subset \mathbb{S}^2$ extends to a homeomorphism of the entire $\mathbb{S}^2.$ We show that there exists a Jordan curve of positive area whose every parametrization via $\mathbb{S}$ admits a homeomorphic extension that has $p$-Sobolev regularity on $\mathbb{S}^2$ for all exponents $1\le p<2 .$ This is obtained via a new sharp extension result for the case of $p<2.$

math.CV↗
arXiv2026

Disproof of a conjecture of Ruscheweyh et al. on universal convexity of Ramanujan generating function

We disprove a conjecture of Ruscheweyh, Salinas and Sugawa concerning the universal convexity of the normalized generating function associated with the Ramanujan sequence $θ(n).$ More precisely, we prove that the function \[ σ(z)=\frac{1}{θ(1)-1/3}\sum_{n\geq1}(θ(n)-1/3)z^{n} \] is not universally convex on the slit domain $\mathbb{C}\backslash[1,\infty).$ The proof uses Watson\textquoteright s integral representation of $θ(n),$ asymptotic estimates for an auxiliary function $h,$ and the representation of derivatives of universally convex functions via logarithmic integrals. As a general extension of this result, we also show that the generalized Ramanujan generating function \[ σ_α(z)=\frac{1}{θ(1)-1/3}\sum_{n\geq1}(θ(n)-1/3)\frac{z^{n}}{n^α} \] is universally convex if and only if $α\geq1.$

math.CV↗