Riemann maps in almost complex manifolds

Notes on quasiregular maps between Riemannian manifolds

These notes provide an exposition on obtaining the well-known standard results of quasiregular maps on Riemannian manifolds, given the corresponding theory in the Euclidean setting. We recall several different approaches to first-order Sobolev spaces between Riemannian manifolds, and show that they result in equivalent definitions of quasiregular maps. We explain how e.g. Reshetnyak's theorem, degree and local index theory, and the quasiregular change of variables formula are transferred into the manifold setting from Euclidean spaces. Finally, we conclude with a proof of the basic fact that p…

关于开放黎曼面全纯映射的曲率估计

A curvature estimate for holomophic maps on open Riemann surfaces

研究利用jet微分技术，对开放黎曼面M的高斯曲率进行估计，该面由一个高分支率的全纯映射诱导出的共形度量构成。

Extensions to the boundary of Riemann maps on varying domains in the complex plane

We give a short proof of the convergence to the boundary of Riemann maps on varying domains. Our proof provides a uniform approach to several ad-hoc constructions that have recently appeared in the literature.

Constructing Strebel differentials via Belyi maps on the Riemann sphere

In this manuscript, by using Belyi maps and dessin d'enfants, we construct some concrete examples of Strebel differentials with four double poles on the Riemann sphere. As an application, we could give some explicit cone spherical metrics on the Riemann sphere.

Some pseudo-Anosov maps on punctured Riemann surfaces represented by multi-twists

This paper has been withdrawn by the author

$λ$-Lemma for families of Riemann surfaces and the critical loci of complex Hénon maps

We prove a version of the classical $λ$-lemma for holomorphic families of Riemann surfaces. We then use it to show that critical loci for complex Hénon maps that are small perturbations of quadratic polynomials with Cantor Julia sets are all quasiconformally equivalent.