[30] Sicheng Lu, Weixu Su: Counting mapping class group orbits under shearing coordinates
Abstract: Let Sg,n be an oriented surface of genus g with n punctures, where 2g−2+n>0 and n>0. Any ideal triangulation of Sg,n induces a global parametrization of the Teichmüller space Tg,n called the shearing coordinates. We study the asymptotics of the number of the mapping class group orbits with respect to the standard Euclidean norm of the shearing coordinates. The result is based on the works of Mirzakhani.
[29] S. Gupta and W. Su, Dominating surface-group representations into PSL2(C) in the relative representation variety . arXiv:2003.13572
Abstract: Let ρ be a representation of the fundamental group of a punctured surface into PSL2(C) that is not Fuchsian. We prove that there exists a Fuchsian representation that strictly dominates ρ in the simple length spectrum, and preserves the boundary lengths. This extends a result of Gueritaud-Kassel-Wolff to the case of PSL2(C)-representations. Our proof involves straightening the pleated plane in H3 determined by the Fock-Goncharov coordinates of a framed representation, and applying strip-deformations.
[28] Su, Weixu; Tan Dong Horospheres in Teichmuller space and mapping class group. arXiv:1801.01812
Abstract: We study the geometry of horospheres in Teichmüller space of Riemann surfaces of genus g with n punctures, where 3g−3+n≥2. We show that every C1-diffeomorphism of Teichmüller space to itself that preserves horospheres is an element of the extended mapping class group. Using the relation between horospheres and metric balls, we obtain a new proof of Royden’s Theorem that the isometry group of the Teichmüller metric is the extended mapping class group.
[27] L.Liu, W. Su and Y. Zhong, Distance and angles between Teichmüller geodesics. Adv. Math. 360 (2020), 106892, 21 pp.
Abstract: We show that the angles between Teichmüller geodesic rays issuing from a common point, defined by using the law of cosines, do not always exist. The proof uses an estimation for the Teichmüller distance on finite dimensional Teichmüller spaces. As a consequence, the Teichmüller space equipped with the Teichmüller metric is not a CAT(k) space for any k∈R. We also discuss some necessary conditions for the existence of angle between the Teichmüller geodesics.
[26] Nguyen, Duc-Manh; Pan, Huiping; Su, Weixu Existence of closed geodesics through a regular point on translation surfaces. Math. Ann. 376 (2020), no. 1-2, 583–607.
Abstract: We show that on any translation surface, if a regular point is contained in some simple closed geodesic, then it is contained in infinitely many simple closed geodesics, whose directions are dense in \({\mathbb {RP}}^1\). Moreover, the set of points that are not contained in any simple closed geodesic is finite. We also construct explicit examples showing that such points exist on some translation surfaces. For a surface in any hyperelliptic component, we show that this finite exceptional set is actually empty. The proofs of our results use Apisa’s classifications of periodic points and of \(\text {GL}(2,{\mathbb {R}})\) orbit closures in hyperelliptic components, as well as a recent result of Eskin–Filip–Wright.
[25] Su, Weixu; Zhong, Youliang; The Finsler geometry of the Teichmüller metric. Eur. J. Math. 3 (2017), no. 4, 1045–1057.
[24] Liu, Lixin; Su, Weixu Variation of extremal length functions on Teichmüller space. Int. Math. Res. Not. IMRN 2017, no. 21, 6411–6443.
Abstract: Extremal length is an important conformal invariant on Riemann surface. It is closely related to the geometry of Teichmüller metric on Teichmüller space. By identifying extremal length functions with energy of harmonic maps from Riemann surfaces to |$\mathbb{R}$|-trees, we study the second variation of extremal length functions along Weil-Petersson geodesics. We show that the extremal length of any measured foliation is a plurisubharmonic function on Teichmüller space.
[23] Liu, L.; Shiga, H.; Su, W.; Zhong, Y. Almost-isometry between the Teichmüller metric and the length-spectrum metric on reduced moduli space for surfaces with boundary. Trans. Amer. Math. Soc. 369 (2017), no. 9, 6429–6464.
[22] Jiang, ManMan; Su, WeiXu Convergence of earthquake and horocycle paths to the boundary of Teichmüller space. Sci. China Math. 59 (2016),no. 10, 1937–1948.
[21] Papadopoulos, Athanase; Su, Weixu Thurston’s metric on Teichmüller space and the translation distances of mapping classes. Ann. Acad. Sci. Fenn. Math. 41 (2016), no. 2, 867–879.
[20] Alessandrini, D.; Liu, L.; Papadopoulos, A.; Su, W. The horofunction compactification of Teichmüller spaces of surfaces with boundary.Topology Appl. 208 (2016), 160–191.
[19] Alberge, Vincent; Papadopoulos, Athanase; Su, Weixu A commentary on Teichmüller’s paper Extremale quasikonforme Abbildungen und quadratische Differentiale. Handbook of Teichmüller theory. Vol. V, 485–531, IRMA Lect. Math. Theor. Phys., 26, Eur. Math. Soc., Zürich, 2016.
[18] Su, Weixu Problems on the Thurston metric. Handbook of Teichmüller theory. Vol. V, 55–72, IRMA Lect. Math. Theor. Phys., 26, Eur. Math. Soc., Zürich, 2016.
[17] Alessandrini, D.; Liu, L.; Papadopoulos, A.; Su, W. On the inclusion of the quasiconformal Teichmüller space into the length-spectrum Teichmüller space. Monatsh. Math. 179 (2016), no. 2, 165–189.
[16] Liu, Lixin; Su, Weixu; Zhong, Youliang On metrics defined by length spectra on Teichmüller spaces of surfaces with boundary. Ann. Acad. Sci. Fenn. Math. 40 (2015), no. 2, 617–644.
[15] Su, Weixu The mapping class group action on the horofunction compactification of Teichmüller space. Handbook of group actions. Vol. I, 249–287, Adv. Lect. Math. (ALM), 31, Int. Press, Somerville, MA, 2015.
[14] Zeng, Jinsong; Su, Weixu Quasisymmetric rigidity of Sierpiński carpets Fn,p. Ergodic Theory Dynam. Systems 35 (2015), no. 5, 1658–1680.
[13] Papadopoulos, A.; Su, W. On the Finsler structure of Teichmüller’s metric and Thurston’s metric. Expo. Math. 33 (2015), no. 1, 30–47.
[12] Papadopoulos, Athanase; Su, Weixu Thurston’s metric on Teichmüller space and isomorphisms between Fuchsian groups. Analysis and geometry of discrete groups and hyperbolic spaces, 95–109, RIMS Kôkyûroku Bessatsu, B48, Res. Inst. Math. Sci. (RIMS), Kyoto, 2014.
[11] Liu, Lixin; Su, Weixu The horofunction compactification of the Teichmüller metric. Handbook of Teichmüller theory. Vol. IV, 355–374, IRMA Lect. Math. Theor. Phys., 19, Eur. Math. Soc., Zürich, 2014.
[10] Liu, L.; Papadopoulos, A.; Su, W.; Théret, G. On the classification of mapping class actions on Thurston’s asymmetric metric. Math. Proc. Cambridge Philos. Soc. 155 (2013), no. 3, 499–515.
[9] Alessandrini, Daniele; Liu, Lixin; Papadopoulos, Athanase; Su, Weixu The behaviour of Fenchel-Nielsen distance under a change of pants decomposition. Comm. Anal. Geom. 20 (2012), no. 2, 369–394.
[8] Alessandrini, D.; Liu, L.; Papadopoulos, A.; Su, W. On local comparison between various metrics on Teichmüller spaces. Geom. Dedicata 157 (2012), 91–110.
[7] Alessandrini, Daniele; Liu, Lixin; Papadopoulos, Athanase; Su, Weixu On various Teichmüller spaces of a surface of infinite topological type.Proc. Amer. Math. Soc. 140 (2012), no. 2, 561–574.
[6] Alessandrini, Daniele; Liu, Lixin; Papadopoulos, Athanase; Su, Weixu; Sun, Zongliang On Fenchel-Nielsen coordinates on Teichmüller spaces of surfaces of infinite type. Ann. Acad. Sci. Fenn. Math. 36 (2011), no. 2, 621–659.
[5] Liu, L.; Su, W. Almost-isometry between Teichmüller metric and length-spectrum metric on moduli space. Bull. Lond. Math. Soc. 43 (2011),no. 6, 1181–1190.
[4] Liu, Lixin; Papadopoulos, Athanase; Su, Weixu; Théret, Guillaume Length spectra and the Teichmüller metric for surfaces with boundary.Monatsh. Math. 161 (2010), no. 3, 295–311.
[3] Liu, Lixin; Papadopoulos, Athanase; Su, Weixu; Théret, Guillaume On length spectrum metrics and weak metrics on Teichmüller spaces of surfaces with boundary. Ann. Acad. Sci. Fenn. Math. 35 (2010), no. 1, 255–274.
[2] Li, Shu Long; Su, Wei Xu; Liu, Li Xin Radial continuity of orientation-preserving maps. (Chinese) Acta Sci. Natur. Univ. Sunyatseni 47(2008), no. 1, 13–15.
