Publications of Ren Guo Ren Guo

    Some of my publications are on Front for the arXiv.
    Preprints
    2015--2018
    • A discrete uniformization theorem for polyhedral surfaces II. (with Xianfeng Gu, Feng Luo, Jian Sun, Tianqi Wu)
      Journal of Differential Geometry 109 (2018), no. 3, 431--466.
    • On a conjecture of Milnor about volume of simplexes. (with Feng Luo)
      Asian Journal of Mathematics 20 (2016), no. 5, 957--968.
    • Survey on Discrete Surface Ricci Flow. (Min Zhang, Wei Zeng, RG, Feng Luo, Xianfeng Gu)
      Journal of Computer Science and Technology, 2015, Vol. 30, Issue (3): 598--613.
    2012--2014
    • Characterizations of hyperbolic geometry among Hilbert geometries.
      Handbook of Hilbert Geometry, pp. 147--158, IRMA Lectures in Mathematics and Theoretical Physics Vol. 22, European Mathematical Society, Zürich, December 2014.
    • The unified discrete surface Ricci flow. (Min Zhang, RG, Wei Zeng, Feng Luo, Shing-Tung Yau, Xianfeng Gu)
      Graphical Models, Volume 76, Issue 5, September 2014, Pages 321--339.
    • A survey of quantum Teichmüller space and Kashaev algebra.
      Handbook of Teichmüller theory. Volume IV, pp. 759--784, IRMA Lectures in Mathematics and Theoretical Physics Vol. 19, European Mathematical Society, Zürich, May 2014.
    • Extremum problems for eigenvalues of discrete Laplace operators.
      Computer Aided Geometric Design, Volume 30, Issue 5, June 2013, Pages 451--461.
    • Discrete heat kernel determines discrete Riemannian metric. (Wei Zeng, RG, Feng Luo, Xianfeng Gu)
      Graphical Models, Volume 74, Issue 4, July 2012, Pages 121--129.
    2011
    • Curvatures on the Teichmüller curve. (with Subhojoy Gupta, Zheng Huang)
      Indiana University Mathematics Journal Vol. 60, No. 5 (2011), 1673--1692.
    • Metric and Heat Kernel.(Wei Zeng, Jian Sun, RG, Feng Luo, Xianfeng Gu)
      Manifold Learning Theory and Applications, Edited by Yun Fu, CRC Press 2011, Pages 145--166.
    • Cell decompositions of Teichmüller spaces of surfaces with boundary. (with Feng Luo)
      Pacific Journal of Mathematics Vol. 253, No. 2 (2011) 423--438.
    • Combinatorial Yamabe flow on hyperbolic surfaces with boundary.
      Communications in Contemporary Mathematics Vol. 13, No. 5 (2011) 827--842.
    • Calculus of generalized hyperbolic tetrahedra.
      Geometriae Dedicata 153 (2011), no. 1, 139--149.
    • Local rigidity of inversive distance circle packing.
      Transactions of the American Mathematical Society 363 (2011), 4757--4776.
    • Cyclic polygons in classical geometry. (with Nilgün Sönmez)
      Comptes rendus de l' Academie bulgare des Sciences, Vol. 64 (2011), no. 2, 185--194.
    2009--2010
    • Quasi-Fuchsian 3-Manifolds and Metrics on Teichmüller Space. (with Zheng Huang, Biao Wang)
      Asian Journal of Mathematics 14 (2010), no. 2, 243--256.
    • On parameterizations of Teichmüller spaces of surfaces with boundary.
      Journal of Differential Geometry 82 (2009), no. 3, 629--640.
    • Rigidity of polyhedral surfaces, II. (with Feng Luo)
      Geometry & Topology 13 (2009), 1265--1312.
    • Quantum Teichmüller space and Kashaev algebra. (with Xiaobo Liu)
      Algebraic & Geometric Topology 9 (2009), 1791--1824.
    • Generalized Discrete Ricci Flow. (Yong-Liang Yang, RG, Feng Luo, Shi-Min Hu, Xianfeng Gu)
      Computer Graphics Forum, Special issue of Pacific Graphics 2009, Vol. 28, No. 7, 2005-2014.
    2004--2008
    • A characterization of hyperbolic geometry among Hilbert geometry.
      Journal of Geometry 89 (2008), no. 1-2, 48--52.
    • A note on circle patterns on surfaces.
      Geometriae Dedicata 125 (2007), 175--190.
    • Geometric angle structures on triangulated surfaces.
      Proceedings of the American Mathematical Society 135 (2007), 3005-3011.
    • Quotient spaces of anti-holomorphic involutions. (with Hongzhu Gao)
      Science in China Series A: Mathematics 48 (2005), no. 12, 1631--1636.
    • Homology classes that can be represented by embedded spheres in rational surfaces. (with Hongzhu Gao)
      Science in China Series A: Mathematics 47 (2004), no. 3, 431--439.