Publications

F. Vargas Pallete. Emedded Delaunay triangulations for point clouds of surfaces in R^3. arXiv:1902.00123 2019.

J. Hass and P. Koehl. Comparing shapes of genus-zero surfaces. Journal of Applied and Computational Topology Volume 1, 57–87 (2017).

P. Koehl. Minimum action principle and shape dynamics. J. Royal Soc. Interface 14:2017031, 2017.

P. Koehl and J. Hass. Landmark-free geometric methods in biological shape analysis. J. Royal Soc. Interface 12:20150795, 2015.

P. Koehl and J. Hass. P. Koehl and J. Hass. Automatic alignment of genus-zero surfaces. IEEE Trans. Pattern Anal. Mach. Intell., 36:466-478, 2014.

A. Tsui, D. Fenton, P. Vuong, J. Hass, P. Koehl, N. Amenta, D. Coeurjolly, C. DeCarli, and O. T. Carmichael. Globally optimal cortical surface matching with exact landmark correspondence. In Proc. Information Processing in Medical Imaging, IPMI 2013, pages 487-498, 2013.

D. Glickenstein and J. Thomas. Duality structures and discrete conformal variations of piecewise constant curvature surfaces. Adv. Math. 320 (2017), 250--278.

D. Glickenstein. A bug's eye view: the Riemannian exponential map on polyhedral surfaces. In Math. Intelligencer 40 (2018), no. 2, 1-9.

S. von Deylan, D. Glickenstein, and M. Wardetzky. Distortion estimates for barycentric coordinates on Riemannian simplices. arXiv:1610.01168 2016.

D. Glickenstein. Euclidean formulation of discrete uniformization of the disk. J. Geom. Imaging Comput. 3 (2016), no. 3-4, 57-80.

D. Champion, D. Glickenstein, and A. Young. Regge's Einstein-Hilbert functional on the double tetrahedron. Differential Geom. Appl. 29 (2011), 109-124.

D. Glickenstein. Discrete conformal variations and scalar curvature on piecewise flat two and three dimensional manifolds. J. Differential Geom. 87 (2011), 201-237.

D. Glickenstein. A monotonicity property for weighted Delaunay triangulations. Discrete Comput. Geom. 38 (2007), no. 4, 651-664.

D. Glickenstein. Geometric duality and discrete Laplacians on manifolds. arXiv:math/0508188v1 2005.

F. Luo. 3-dimensional Schläfli formula and its generalization. arXiv:0802.2580 (2008).

F. Luo. A characterization of spherical polyhedral surfaces. Journal of Differential Geometry (2006): 407-424.

F. Luo. A combinatorial curvature flow for compact 3-manifolds with boundary. Electronic Research Announcements of the American Mathematical Society 11.2 (2005): 12-20.

F. Luo and S. Tillmann. Angle structures and normal surfaces. Transactions of the American Mathematical Society 360.6 (2008): 2849-2866.

B. Chow and F. Luo. Combinatorial Ricci flows on surfaces. Journal of Differential Geometry 63.1 (2003): 97-129.

F. Luo. Combinatorial Yamabe flow on surfaces. Communications in Contemporary Mathematics 6.05 (2004): 765-780.

X. Gu, F. Luo and S.T. Yau. Computational Conformal Geometry Behind Modern Technologies Notices of the American Mathematical Society Nov. (2020): 1509-1525.

F. Luo. Continuity of the volume of simplices in classical geometry. Communications in Contemporary Mathematics 8.03 (2006): 411-431.

M. Jin, J. Kim, F. Luo and X. Gu. Discrete surface Ricci flow. IEEE Transactions on Visualization and Computer Graphics 14(5) (2008): 1030-1043.

R. Sarkar, X. Yin, J. Gao, F. Luo and X. Gu. Greedy routing with guaranteed delivery using ricci flows. International Conference on Information Processing in Sensor Networks. IEEE (2009): 121-132.

X. Gu, Y. He, M. Jin, F. Luo, H. Qin and S.T. Yau. Manifold splines with a single extraordinary point. Computer-Aided Design 40.6 (2008): 676-690.

F. Luo. On Teichmüller spaces of surfaces with boundary. Duke Mathematical Journal 139.3 (2007): 463-482.

X. Gu, F. Luo and S.T. Yau. Recent advances in computational conformal geometry. IMA International Conference on Mathematics of Surfaces. Springer, Berlin, Heidelberg, 2009.

F. Luo. Rigidity of polyhedral surfaces, I. Journal of Differential Geometry 96.2 (2014): 241-302.

R. Guo and F. Luo. Rigidity of polyhedral surfaces, II. Geometry & Topology 13.3 (2009): 1265-1312.

F. Luo. Solving Thurston's equation in a commutative ring. Journal of Topology 9.1 (2016): 143-160.

F. Luo. Volume and angle structures on 3-manifolds. Asian Journal of Mathematics 11.4 (2007): 555-566.

F. Luo. Volume optimization, normal surfaces, and Thurston's equation on triangulated 3-manifolds. Journal of Differential Geometry 93.2 (2013): 299-326.

T. Wu and S.T. Yau. Computing Harmonic Maps and Conformal Maps on Point Clouds. arXiv:2009.09383 (2020).

T. Wu and X. Zhu. The Convergence of Discrete Uniformizations for Closed Surfaces. arXiv:2008.06744 (2020).

F. Luo and T. Wu. Koebe conjecture and the Weyl problem for convex surfaces in hyperbolic 3-space. arXiv:1910.08001 (2019).

X. Gu, F. Luo and T. Wu. Convergence of discrete conformal geometry and computation of uniformization maps. Asian Journal of Mathematics 23.1 (2019): 21-34.

X. Gu, R. Guo, F. Luo, J. Sun and T. Wu. A discrete uniformization theorem for polyhedral surfaces II. Journal of differential geometry 109.3 (2018): 431-466.

X. Gu, F. Luo, J. Sun and T. Wu. A discrete uniformization theorem for polyhedral surfaces. Journal of differential geometry 109.2 (2018): 223-256.

J. Sun, T. Wu, X. Gu and F. Luo. Discrete Conformal Deformation: Algorithm and Experiments SIAM Journal on Imaging Sciences 8.3 (2015): 1421-1456.

T. Wu, X. Gu and J. Sun. Rigidity of infinite hexagonal triangulation of the plane. Transactions of the American Mathematical Society 367.9 (2015): 6539-6555.

J. Hass and M. Trnkova, Approximating isosurfaces by guaranteed-quality triangular meshes. Eurographics 39, Number 5, (2020): 29–40.

T. Doehrman and D. Glickenstein, Determinant of the finite volume Laplacian. arXiv:2108.07308





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