arXiv subjects

Yaxiang Li

Publications and source records attributed to Yaxiang Li.

20 records · Page 2Linked to original sources

arXiv2012

On quasimöbius maps in real Banach spaces

Suppose that $E$ and $E'$ denote real Banach spaces with dimension at least 2, that $D\varsubsetneq E$ and $D'\varsubsetneq E'$ are domains, that $f: D\to D'$ is an $(M,C)$-CQH homeomorphism, and that $D$ is uniform. The main aim of this paper is to prove that $D'$ is a uniform domain if and only if $f$ extends to a homeomorphism $\bar{f}: \bar{D}\to \bar{D}'$ and $\bar{f}$ is $η$-QM relative to $\partial D$. This result shows that the answer to one of the open problems raised by Väisälä from 1991 is affirmative.

math.CV↗

arXiv2012

Local properties of quasihyperbolic and freely quasiconformal mappings

Suppose that $E$ and $E'$ denote real Banach spaces with dimension at least 2, that $D\subset E$ and $D'\subset E'$ are domains, and that $f: D\to D'$ is a homeomorphism. In this paper, we prove that if there exists some constant $M>1$ (resp. some homeomorphism $ϕ$) such that for all $x\in D$, $f: B(x,d_D(x))\to f(B(x,d_D(x)))$ is $M$-QH (resp. $ϕ$-FQC), then $f$ is $M_1$-QH with $M_1=M_1(M)$ (resp. $ϕ_1$-FQC with $ϕ_1=ϕ_1(ϕ)$). We apply our results to establish, in terms of the $j_D$ metric, a sufficient condition for a homeomorphism to be FQC.

math.MG↗