Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2403.10811

Analytic functions with hyperbolic range and Bohr's inequality

Yusuf Abu Muhanna·Issam Louhichi
View original source ↗Read source document ↗Export metadata ↓

Abstract

We use properties of the hyperbolic metric and properties of the modular function to show that the Bohr's radius for covering maps onto hyperbolic domains is greater or equal to exponential minus pi. This includes almost all known classes of analytic functions.

Explore related subjects

math.MG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yusuf Abu Muhanna, Issam Louhichi. 2024-03-16. Analytic functions with hyperbolic range and Bohr's inequality. https://arxiv.org/abs/2403.10811

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

KEEP EXPLORING

Related papers

arXiv2026

$β$-Uniform Convexity and Divisible Domains

Divisible convex sets have long been important in the study of Hilbert geometries. When a divisible convex set is an ellipsoid, the Hilbert geometry it induces is the hyperbolic space. In general, strictly convex divisible domains exhibit negative curvature properties, but only the ellipsoid is a CAT(0) space. The notion of p-uniform convexity from the theory of Banach spaces has been proposed by Shin-Ichi Ohta as a generalization of the Alexandrov-Toponogov comparison theorems to Finsler manifolds. We prove that a natural Finsler metric on a strictly convex divisible domain is $β$-uniformly convex, where the constant $β$ is related to the regularity of the boundary. We use this to show, with AI assistance, that the Hilbert metric, under suitable local and scale-dependent assumptions, is $β$-uniformly convex on such domains.

math.MG↗
arXiv2026

A positive solution to the $L^p$ projection centroid conjecture

In a classical paper [21] in 2000, Lutwak-Yang-Zhang established the $L^p$ analog of the Petty projection inequality and the $L^p$ analog of the Busemann-Petty centroid inequality. In Section 7 of [21], Lutwak-Yang-Zhang proposed the important $L^p$ projection centroid conjecture. We give a positive solution to the $L^p$ projection centroid conjecture in this work.

math.MG↗
arXiv2026

Minimal central slices of the regular simplex

We prove that minimal-volume hyperplane sections of the regular simplex through its centroid are parallel to a facet. The proof combines variational methods with Fourier-analytic techniques and zero-diminishing arguments to show that every critical normal vector has at most three distinct non-zero coordinates. Analysis of the two- and three-value cases then yields the sharp lower bound.

math.MG↗