Publications of Ren Guo

Some of my publications are on Front for the arXiv.

**Preprints**

- 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.

**2015--2018**

- 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.

**2012--2014**

- 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.

**2011**

- 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.

**2009--2010**

- 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.

**2004--2008**