Manzi Huang

activity

20112025

most citedOn Lipschitz continuity of solutions of hyperbolic Poisson's equation

24 citations · 30 across the 19 of their papers we have counts for

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12 papers · 1 filter

math.CV2025

Characterizations of quasihyperbolic John domains and uniform domains in metric spaces

Shu-Jing Gao, Chang-Yu Guo, Manzi Huang +1

In a recent work of Zhou and Ponnusamy [Ann. Sc. Norm. Super. Pisa Ci. Sci. 2025], the authors studied the following natural question: find sufficient and necessary conditions for…

math.CV2025

Gromov hyperbolicity III: an improved geometric characterization and its applications

Chang-Yu Guo, Manzi Huang, Xiantao Wang

In the seminal work of Balogh-Buckley [Invent. Math. 2003], the authors asked the following fundamental open problem: for proper subdomains in the Euclidean space $R^{n}$ , d…

math.CV2025

Dimension-free inner uniform estimates for quasigeodesics

Chang-Yu Guo, Manzi Huang, Yaxiang Li +1

In this paper, we establish a dimension-free inner uniform estimate for quasigeodesics. More precisely, we prove that a $c_{0}$ -quasigeodesic in a $δ$ -Gromov hyperbolic $c$ -John doma…

math.CV2025

The dimension-free Gehring-Hayman inequality for quasigeodesics

Chang-Yu Guo, Manzi Huang, Xiantao Wang

A well-known theorem of J. Heinonen and S. Rohde in 1993 states that if $D \subset R^{n}$ is quasiconformally equivalently to an uniform domain, then the Gehring-Hayman inequ…

math.CV2023

Isoperimetric type inequalities for mappings induced by weighted Laplace differential operators

Jiaolong Chen, Shaolin Chen, Manzi Huang +1

The main purpose of this paper is to establish some isoperimetric type inequalities for mappings induced by the weighted Laplace differential operators. The obtained results of thi…

math.CV2017

Geometric characterizations of inner uniformity through Gromov hyperbolicity

Manzi Huang, Antti Rasila, Xiantao Wang +1

In this paper, we study the characterization of inner uniformity of bounded domains $G$ in $\IR^n$, and prove that the following three conditions are equivalent: $(1)$ $G$ is inner…

math.CV2015

On the subinvariance of uniform domains in metric spaces

Yaxiang Li, Manzi Huang, Xiantao Wang +1

Suppose that $X$ and $Y$ are quasiconvex and complete metric spaces, that $G \subset X$ and $G^{'} \subset Y$ are domains, and that $f : G \to G^{'}$ is a homeomorphism. Our main result is t…

math.CV2014★ 2 cited

Semisolidity and locally weak quasisymmetry of homeomorphisms in metric spaces

Manzi Huang, Antti Rasila, Xiantao Wang +1

In this paper, we investigate the relationship between semisolidity and locally weak quasisymmetry of homeomorphisms in quasiconvex and complete metric spaces. Our main objectives…

math.CV2012

On bilipschitz extensions in real Banach spaces

Manzi Huang, Yaxiang Li

Suppose that $E$ and $E^{'}$ denote real Banach spaces with dimension at least 2, that $D \neq = E$ and $D^{'} \neq = E^{'}$ are bounded domains with connected boundaries, that $f : D \to D^{'}$ is an…

math.CV2012

Mapping problems for quasiregular mappings

Manzi Huang, Antti Rasila, Xiantao Wang

We study images of the unit ball under certain special classes of quasiregular mappings. For homeomorphic, i.e., quasiconformal mappings problems of this type have been studied ext…

math.CV2012★ 1 cited

On quasisymmetry of quasiconformal mappings and its applications

M. Huang, S. Ponnusamy, A. Rasila +1

Suppose that $f : D \to D^{'}$ is a quasiconformal mapping, where $D$ and $D^{'}$ are domains in $R^{n}$ , and that $D$ is a broad domain. Then for every arcwise connected subset $A…

math.CV2011★ 2 cited

On quasimöbius maps in real Banach spaces

Manzi Huang, Yaxiang Li, Matti Vuorinen +1

Suppose that $E$ and $E^{'}$ denote real Banach spaces with dimension at least 2, that $D  E$ and $D^{'}  E^{'}$ are domains, that $f : D \to D^{'}$ is an $(M, C)$ -CQH hom…