Belkin, M. and Niyogi, P.. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation, 15(6):1373–1396, 2003.
Belkin, M. and Niyogi, P.. Towards a theoretical foundation for laplacian-based manifold methods. In COLT, pages 486–500, 2005.
Belkin, M. and Niyogi, P.. Convergence of laplacian eigenmaps. preprint, short version NIPS 2008, 2008.
Belkin, M., Sun, J., and Wang, Y.. Constructing laplace operator from point clouds in rd. In SODA ′09: Proceedings of the Nineteenth Annual ACM -SIAM Symposium on Discrete Algorithms, pages 1031–1040, Philadelphia, PA, USA, 2009. Society for Industrial and Applied Mathematics.
Bertalmio, M., Cheng, L.-T., Osher, S., and Sapiro, G.. Variational problems and partial differential equations on implicit surfaces. Journal of Computational Physics, 174(2):759–780, 2001.
Bertalmio, M., Memoli, F., Cheng, L.-T., Sapiro, G., and Osher, S.. Variational problems and partial differential equations on implicit surfaces: Bye bye triangulated surfaces? In Geometric Level Set Methods in Imaging, Vision, and Graphics, pages 381–397. Springer
New York, 2003.
Cao, H.-D. and Yau, S.-T.. Geometric flows, volume 12 of Surveys in Differential Geometry. International Press of Boston, Inc., 2007.
da Costa, R. C. T.. Quantum mechanics of a constrained particle. PHYSICAL REVIEW A, 25(6), April 1981.
Defay, R. and Priogine, I.. Surface Tension and Adsorption. John Wiley & Sons, New York, 1966.
Dey, T. K.. Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics). Cambridge University Press, New York, NY, USA, 2006.
Dey, T. K., Ranjan, P., and Wang, Y.. Convergence, stability, and discrete approximation of laplace spectra. In Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ′10, pages 650–663, Philadelphia, PA, USA, 2010. Society for Industrial and Applied Mathematics.
Dodziuk, J. and Patodi, V. K.. Riemannian structures and triangulations of manifolds. Journal of Indian Math. Soc., 40:152, 1976.
Dziuk, G.. Finite elements for the beltrami operator on arbitrary surfaces. In Hildebrandt, S. and Leis, R., editors, Partial differential equations and calculus of variations, volume 1357 of Lecture Notes in Mathematics, pages 142–155. Springer, 1988.
Hein, M., Audibert, J.-Y., and von Luxburg, U.. From graphs to manifolds - weak and strong pointwise consistency of graph laplacians. In Proceedings of the 18th Annual Conference on Learning Theory, COLT’05, pages 470–485, Berlin, Heidelberg, 2005. Springer-Verlag.
Jean-Daniel Boissonnat, A. G., Dyer, Ramsay. Stability of delaunay-type structures for manifolds: [extended abstract]. In Symposium on Computational Geometry, pages 229–238, 2012.
Lafon, S.. Diffusion Maps and Geometric Harmonics. PhD thesis, 2004.
Lai, R., Liang, J., and Zhao, H.. A local mesh method for solving pdes on point clouds. Inverse Problem and Imaging, to appear.
Levy, B.. Laplace-beltrami eigenfunctions towards an algorithm that “understands” geometry. In Shape Modeling and Applications, 2006. SMI 2006. IEEE International Conference on, pages 13–13, June 2006.
Liang, J. and Zhao, H.. Solving partial differential equations on point clouds. SIAM Journal of Scientific Computing, 35:1461–1486, 2013.
Lindeberg, T.. Scale selection properties of generalized scale-space interest point detectors. Journal of Mathematical Imaging and Vision, 46(2):177–210, 2013.
Luo, C., Sun, J., and Wang, Y.. Integral estimation from point cloud in d-dimensional space: a geometric view. In Symposium on Computational Geometry, pages 116–124, 2009.
Macdonald, C. B. and Ruuth, S. J.. The implicit closest point method for the numerical solution of partial differential equations on surfaces. SIAM J. Sci. Comput., 31(6):4330–4350, 2009.
März, T. and Macdonald, C. B.. Calculus on surfacewith feneral closest point functions. SIAM J. Numer. Anal., 50(6):3303–3328, 2012.
Ovsjanikov, M., Sun, J., and Guibas, L. J.. Global intrinsic symmetries of shapes. Comput. Graph. Forum, 27(5):1341–1348, 2008.
Reuter, M., Wolter, F.-E., and Peinecke, N.. Laplace-beltrami spectra as “shape-dna” of surfaces and solids. Computer-Aided Design, 38(4):342–366, 2006.
Ruuth, S. J. and Merriman, B.. A simple embedding method for solving partial differential equations on surfaces. Journal of Computational Physics, 227(3):1943–1961, 2008.
Saito, N.. Data analysis and representation on a general domain using eigenfunctions of laplacian. Applied and Computational Harmonic Analysis, 25(1):68–97, 2008.
Schuster, P. and Jaffe, R.. Quantum mechanics on manifolds embedded in euclidean space. Annals of Physics, 307(1):132–143, 2003.
Shewchuk, J. R.. Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. In Lin, M. C. and Manocha, D., editors, Applied Computational Geometry: Towards Geometric Engineering, volume 1148 of Lecture Notes in Computer Science, pages 203–222. Springer-Verlag, May 1996. From the First ACM Workshop on Applied Computational Geometry.
Shewchuk, J. R.. What is a good linear finite element? - interpolation, conditioning, anisotropy, and quality measures. Technical report, In Proc. of the 11th International Meshing Roundtable, 2002.
Shi, Z. and Sun, J.. Convergence of laplacian spectra from point clouds. arXiv:1506.01788.
Shi, Z. and Sun, J.. Convergence of the point integral method for the poisson equation on manifolds i: the neumann boundary. arXiv:1403.2141.
Shi, Z. and Sun, J.. Convergence of the point integral method for the poisson equation on manifolds ii: the dirichlet boundary. arXiv:1312.4424.
Singer, A. and tieng Wu, H.. Spectral convergence of the connection laplacian from random samples. arXiv:1306.1587.
Strang, G. and Fix, G. J.. An analysis of the finite element method. Prentice-Hall, 1973.
 The CGAL Project. CGAL User and Reference Manual. CGAL Editorial Board, 4.4 edition, 2014.
Wardetzky, M.. Discrete Differential Operators on Polyhedral Surfaces - Convergence and Approximation. PhD thesis, 2006.
Yau, S.-T.. The role of partial differential equations in differential geometry. In Proceedings of the International Congress of Mathematicians (Helsinki 1978), pages 237–250. Acad. Sci. Fennica, Helsinki, 1980.