Vladimir Markovi'c

activity

20242026

collaborators

6 papers

math.GT2026

Simple geodesics in closed hyperbolic manifolds

Qiliang Luo, Vladimir Marković

Given any closed hyperbolic n-manifold M ( $n \geq 3$ ), we show that for a fixed $κ > \frac{3}{n - 2}$ , a random closed geodesic of length close to r has the collar of width $r^{- κ}$ when…

math.DG2026

Harmonic extension of Weil-Petersson circle homeomorphisms

Farid Diaf, Vladimir Marković, Abderrahim Mesbah

In this paper, we study Weil--Petersson circle homeomorphisms from the viewpoint of harmonic maps. We prove that a homeomorphism $φ : S^{1} \to S^{1}$ is Weil--Petersson if…

math.GT2026

Holomorphic curves in compact quotients of SL(2,C)

Yiran Lin, Vladimir Markovic

We prove that every discrete faithful representation of the surfcae group into SL(2,C) is the monodromy of a holomorphic connection on the trivial rank-2 vector bundle over a Riema…

math.CV2025

Unique extremality of affine maps on plane domains

Qiliang Luo, Vladimir Marković

We prove that affine maps are uniquely extremal quasiconformal maps on the complement of a well distribute set in the complex plane answering a conjecture from \cite{markovic}. We…

math.AG2024

Derivative of the Riemann-Hilbert map

Vladimir Marković, Ognjen Tošić

Given a pair $(X, \nabla)$ , consisting of a closed Riemann surface $X$ and a holomorphic connection $\nabla$ on the trivial principal bundle $X \times SL_{2} (C) \to X$ ,…

math.GT2024

Tangle free permutations and the Putman-Wieland property of Random covers

Adam Klukowski, Vladimir Marković

Let $Σ_{g}^{p}$ denote a surface of genus $g$ and with $p$ punctures. Our main result is that the fraction of degree $n$ covers of $Σ_{g}^{p}$ which have the Putman-Wieland property tends…