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Some Remarks on Teichmüller spaces and Modular Groups

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Acta Mathematica Sinica,English Series 2009年第8期25卷 1289-1296页

作者： Yun HU Department of Mathematics Soochow University Suzhou 215006 P. R. China

We study the fixed point sets of subgroups of modular groups acting on teichmiiller spaces.

关键词： teichmiiller space modular group allowable mapping

Convergence of earthquake and horocycle paths to the boundary of Teichm¨uller space

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Science China Mathematics 2016年第10期59卷 1937-1948页

作者： JIANG ManMan SU WeiXu Department of Mathematics Sun Yat-sen UniversityGuangzhou 510275China School of Mathematical Sciences Fudan UniversityShanghai 200433China Shanghai Center for Mathematical Sciences Shanghai 200433China

We study the convergence of earthquake paths and horocycle paths in the Gardiner-Masur compact- ification of Teichmfiller space. We show that an earthquake path directed by a uniquely ergodic or simple closed measured geodesic lamination converges to the Gardiner-Masur boundary. Using the embedding of flat metrics into the space of geodesic currents, we prove that a horocycle path in teichmiiller space, which is induced by a quadratic differential whose vertical measured foliation is uniquely ergodic, converges to the Gardiner-Masur boundary and to the Thurston boundary.

关键词： earthquake Gardiner-Masur boundary horocycle flow teichmiiller space

Geometric aspects of the moduli space of Riemann surfaces

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Science China Mathematics 2005年第Z1期48卷 97-122页

作者： Shing-Tung Yau Department of Mathematics Harvard University CambridgeMA 02138USA

We describe some recent progress in the study of moduli space of Riemann surfaces in this survey paper. New complete Kahler metrics were introduced on the moduli space and Teichmuller space. Their curvature properties and asymptotic behavior were studied in details. These natural metrics served as bridges to connect all the known canonical metrics, especially the Kahler-Einstein metric. We showed that all the known complete metrics on the moduli space are equivalent and have Poincare type growth. Furthermore,the Kahler-Einstein metric has strongly bounded geometry. This also implied that the logarithm cotangent bundle of the moduli space is stable in the sense of Mumford.

关键词： moduli space teichmiiller space metric curvature.

The generalized main inequality of Reich-Strebel and its applications

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Science China Mathematics 2014年第2期57卷 333-341页

作者： LI Zhong QI Yi School of Mathematical Sciences Peking University School of Mathematics and Systems Science Beihang University

In this paper,a new version of the general form of the main inequality of Reich-Strebel is *** applications,we improve the strong triangle inequality and generalize the Delta inequality in certain sense.

关键词： main inequality teichmiiller space quasiconformal mappings

Hausdorff dimension of quasi-cirles of polygonal mappings and its applications

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Science China Mathematics 2013年第5期56卷 1033-1040页

作者： HUO ShengJin TANG ShuAn WU ShengJian LMAM and School of Mathematical Sciences Peking University School of Mathematics and Computer Science Guizhou Normal University

We show that the Hausdorff dimension of quasi-circles of polygonal mappings is one. Furthermore, we apply this result to the theory of extremal quasiconformal mappings. Let [μ] be a point in the universal teichmiiller space such that the Hausdorff dimension of fμ（δ△） is bigger than one. We show that for every kn ∈ （0, 1） and polygonal differentials δn, n = 1, 2, the sequence {[kn δn/｜δn｜} cannot converge to [μ] under the teichmiiller metric.

关键词： Hausdorff dimension teichmiiller space quasi-circle polygonal mapping