arXiv subjects

Vlad Markovic

Publications and source records attributed to Vlad Markovic.

2 recordsLinked to original sources

arXiv2014

Quasiconformal Homogeneity of Genus Zero Surfaces

A Riemann surface $M$ is said to be $K$-quasiconformally homogeneous if for every two points $p,q \in M$, there exists a $K$-quasiconformal homeomorphism $f \colon M \rightarrow M$ such that $f(p) = q$. In this paper, we show there exists a universal constant $K_0 > 1$ such that if $M$ is a $K$-quasiconformally homogeneous hyperbolic genus zero surface other than the disk $\mathbb{D}$, then $K \geq K_0$. This answers a question by Gehring and Palka.

math.GT↗

arXiv2009

Topological Entropy and Diffeomorphisms of Surfaces with Wandering Domains

Let $M$ be a closed surface and $f$ a diffeomorphism of $M$. A diffeomorphism is said to permute a dense collection of domains, if the union of the domains are dense and the iterates of any one domain are mutually disjoint. In this note, we show that if $f \in \diff^{1+α}(M)$, with $α>0$, and permutes a dense collection of domains with bounded geometry, then $f$ has zero topological entropy.

math.DS↗