Let T0（Δ） be the subset of the universal Teichm¨uller space, which consists all of the elements with boundary dilatation 1. Let SQ（Δ） be the unit ball of the space Q（Δ） of all integrable holomorphic quad...Let T0（Δ） be the subset of the universal Teichm¨uller space, which consists all of the elements with boundary dilatation 1. Let SQ（Δ） be the unit ball of the space Q（Δ） of all integrable holomorphic quadratic differentials on the unit disk Δ and Q0（Δ） be defined as Q0（Δ） = {？ ∈ SQ（Δ） ： there exists a k ∈（0, 1） such that [kˉ？ ｜？｜] ∈ T0（Δ）}. In this paper, we show that Q0（Δ） is dense in SQ（Δ）.展开更多
This paper focuses on Teichmüller curves in the space of two-genus double covers of flat tori,identifying all of them, counting them with respect to their triangular areas, formulating the numbers of their cusps,...This paper focuses on Teichmüller curves in the space of two-genus double covers of flat tori,identifying all of them, counting them with respect to their triangular areas, formulating the numbers of their cusps, and characterizing the ones without a simple cusp. Some applications are also discussed.展开更多
Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius tran...Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius transformations preserving the unit disk.We study several distortion properties for diffeomorphisms and quasisymmetric homeomorphisms.Using these distortion properties,we give the Bers complex manifold structure on the Teichm(u| ")ller space TC^1+H as the union of over all0 <α≤1,which turns out to be the largest space in the Teichmuller space of C1 orientation-preserving circle diffeomorphisms on which we can assign such a structure.Furthermore,we prove that with the Bers complex manifold structure on TC^1+H ,Kobayashi’s metric and Teichmuller’s metric coincide.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11371035)
文摘Let T0（Δ） be the subset of the universal Teichm¨uller space, which consists all of the elements with boundary dilatation 1. Let SQ（Δ） be the unit ball of the space Q（Δ） of all integrable holomorphic quadratic differentials on the unit disk Δ and Q0（Δ） be defined as Q0（Δ） = {？ ∈ SQ（Δ） ： there exists a k ∈（0, 1） such that [kˉ？ ｜？｜] ∈ T0（Δ）}. In this paper, we show that Q0（Δ） is dense in SQ（Δ）.
基金supported by National Natural Science Foundation of China (Grant No. 11401167).supported by National Natural Science Foundation of China (Grant No. 11371035).supported by National Natural Science Foundation of China (Grant Nos. 11701039 and 11371035)Research and Innovation Program of Beijing University of Posts and Telecommunications for Youth (Grant No. 2017RC18)
文摘This paper focuses on Teichmüller curves in the space of two-genus double covers of flat tori,identifying all of them, counting them with respect to their triangular areas, formulating the numbers of their cusps, and characterizing the ones without a simple cusp. Some applications are also discussed.
基金supported by the National Science Foundationsupported by a collaboration grant from the Simons Foundation(Grant No.523341)PSC-CUNY awards and a grant from NSFC(Grant No.11571122)。
文摘Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius transformations preserving the unit disk.We study several distortion properties for diffeomorphisms and quasisymmetric homeomorphisms.Using these distortion properties,we give the Bers complex manifold structure on the Teichm(u| ")ller space TC^1+H as the union of over all0 <α≤1,which turns out to be the largest space in the Teichmuller space of C1 orientation-preserving circle diffeomorphisms on which we can assign such a structure.Furthermore,we prove that with the Bers complex manifold structure on TC^1+H ,Kobayashi’s metric and Teichmuller’s metric coincide.
