Alexander I. Bobenko, Yuri B. Suris, Discrete Differential Geometry: Integrable Structure

A.I. Bobenko, A.Y. Fairley, Nets of lines with the combinatorics of the square grid and with touching inscribed conics (2019) arXiv:1911.08477 [math.AG]

A.I. Bobenko, T. Hoffmann, T. Rörig, Orthogonal ring patterns (2019) arXiv:1911.07095 [math.CV]

A.V. Akopyan, A.I. Bobenko, W.K. Schief, J. Techter, On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs (2019) arXiv:1908.00856 [math.DG]

A.I. Bobenko, U. Bücking, Convergence of discrete period matrices and discrete holomorphic integrals for ramified coverings of the Riemann sphere (2018) arXiv:1809.04847 [math.CV]

A.I. Bobenko, H. Pottmann, T. Rörig, Multi-nets. Classification of discrete and smooth surfaces with characteristic properties on arbitrary parameter rectangles, Discrete and Comp. Geometry (2019), doi.org/10.1007/s00454-019-00101-1, Preprint (2018) arXiv:1802.05063 [math.DG]

A.I. Bobenko, W.K. Schief, J. Techter, Checkerboard incircular nets. Laguerre geometry and parametrization, Geometriae Dedicata 204:1 (2020), 97-129, doi.org/10.1007/s10711-019-00449-x, Preprint (2018) arXiv:1808.07254 [math.DG]

A.I. Bobenko, S. Tsarev, The curvature line parametrization from circular nets on a surface. Journal of Mathematical Physics (2018) 59, 091410, doi:10.1063/1.5041257

A. Akopyan, A.I. Bobenko, Incircular nets and confocal conics, Trans. AMS 370:4 (2018), 2825-2854, Preprint (2016) arXiv:1602.04637 [math.MG]

A.I. Bobenko, U. Bücking, S. Sechelmann, Discrete minimal surfaces of Koebe type, In: Modern Approaches to Discrete Curvature, L. Najman, P. Romon (eds.), Lect. Notes in Math., v. 2184, Springer, 2017, 259-291

A.I. Bobenko, P. Romon, Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. A discrete Lawson correnspondence. Journal of Integrable Systems (2017) Volume 2:1, 1-18, doi:10.1093/integr/xyz010, Preprint (2017) arXiv:1705.01053 [math.DG]

A.I. Bobenko, W. Schief, Yu.B. Suris, J. Techter. On a discretization of confocal quadrics. II. A geometric approach to general parametrizations. arXiv:1708.06800 [math.DG]

A.I. Bobenko, F. Günther, Discrete Riemann surfaces based on quadrilateral cellular decompositions, Advances in Mathematics,Volume 311, (2017), 885–932, Preprint (2015) arXiv:1511.00652 [math.CV]

A.I. Bobenko, N. Dimitrov, S. Sechelmann, Discrete uniformization of polyhedral surfaces with non-positive curvature and branched covers over the sphere via hyper-ideal circle patterns, Discrete and Computational Geometry, v. 57, (2017), 431-469, Preprint (2015) arXiv:1510.04053 [math.MG]

A.I. Bobenko, S. Sechelmann, B. Springborn, Discrete conformal maps: Boundary value problems, cirlce domains, Fuchsian and Schottky uniformizations, In: Advances in Discrete Differential Geometry, A.I. Bobenko (ed.), Springer, 2016, 1-56

A.I. Bobenko, F. Günther, Discrete complex analysis on planar quad-graphs, In: Advances in Discrete Differential Geometry, A.I. Bobenko (ed.), Springer, 2016, 57-132, Preprint (2015) arXiv:1505.05673 [math.CV]

A.I. Bobenko, T. Hoffmann, S-conical CMC surfaces. Towards a unified theory of discrete surfaces with constant mean curvature, In: Advances in Discrete Differential Geometry, A.I. Bobenko (ed.), Springer, 2016, 287-308

Yu.B. Suris. Billiards in confocal quadrics as a pluri-Lagrangian system. Theor. and Appl. Mech., 2016, 43, No. 2, p. 221-228. arXiv:1511.06123 [nlin.SI]

A.I. Bobenko, W.K. Schief, Yu.B. Suris, J. Techter, On a discretization of confocal quadrics. I. An integrable systems approach, Journal of Integrable Systems (2016) Volume 1:1, 1-34, doi:10.1093/integr/xyz005 , Preprint (2016) arXiv:1511.01777 [math.DG]

Yu.B. Suris. The Erlangen Program and discrete differential geometry. - In: Sophus Lie and Felix Klein: The Erlangen Program and its Impact in Mathematics and Physics, Eds. L. Ji and A. Papadopoulos, IRMA Lectures in Mathematics and Theoretical Physics 23, European Mathematical Society, 2015, p. 247-279. Book on the Publisher's site

A.I. Bobenko, W.K. Schief, Circle complexes and the discrete CKP equation, Internat. Math. Research Notices, vol. 2017(5), 1504-1561, Preprint (2015) arXiv:1509.04109 [math.DG]

A.I. Bobenko, E. Huhnen-Venedey, T. Rörig, Supersyclidic nets, Internat. Math. Research Notices, vol. 2017 (2), 323-371, Preprint (2014) arXiv:1412.7422 [math.DG]

A.I. Bobenko, U. Hertrich-Jeromin, I. Lukyanenko, Discrete constant mean curvature nets in space forms:
Steiner's formula and Christoffel duality, Discrete and Computational Geometry (2014) 52, 612-629, Preprint (2014) arXiv:1409.2001 [math.DG]

A.I. Bobenko, U. Pinkall, B. Springborn, Discrete conformal maps and ideal hyperbolic polyhedra, Geometry and Topology., 19, (2015), 2155-2215, Prerpint (2010) arXiv:1005.2698 [math.GT]

A.I. Bobenko, M. Skopenkov, Discrete Riemann surfaces: linear discretization and its convergence, J. reine und angew. Math.,720, (2016), 217-250, Preprint (2012) arXiv:1210.0561 [math.CV]

M. Petrera, Yu.B. Suris. Spherical geometry and integrable systems. Geometriae Dedicata, 2014, 169, No. 1, p. 83-98. arXiv:1208.3625 [math-ph]

A.I. Bobenko, B. Springborn, Diskretisierung in Geometrie und Dynamik - Elastische Stäbe und Rauchringe, Mitteilungen der DMV, 21(4), (2013), 218-224

A.I. Bobenko, E. Huhnen-Venedey, Curvature line parametrized surfaces and orthogonal coordinate systems. Discretization with Dupin cyclides, Geometria Dedicata (2012), 159:1, 207-237 , Preprint (2011) arXiv:1101.5955 [math.DG]

A.I. Bobenko, Ch. Mercat, M. Schmies, Conformal Structures and Period Matrices of Polyhedral Surfaces, In: Computational Approach to Riemann Surfaces, A.I. Bobenko, Ch. Klein (Eds.), Lecture Notes in Mathematics, Vol. 2013, Springer, 2011, 213-226, Preprint (2009) arXiv:0909.1305 [math.DG]   [pdf file]

A.I. Bobenko, H. Pottmann, J. Wallner, A curvature theory for discrete surfaces based on mesh parallelity, Math. Annalen 348 (2010), 1-24,  Preprint (2009) arXiv:0901.4620 [math.DG]  [pdf file]

A.I. Bobenko, Yu.B. Suris, Discrete Koenigs nets and discrete isothermic surfaces, Internat. Math. Research Notices (2009) 1976-2012, Preprint (2007) arXiv:0709.3408 [math.DG]   [pdf file]

A.I. Bobenko, Yu.B. Suris, Linear integrable systems on quad-graphs (2019) arXiv:1911.03252 [math-ph]

A.Sridhar, Yu.B. Suris. Commutativity in Lagrangian and Hamiltonian mechanics. arXiv:1801.06076 [math-ph]

M. Petrera, Yu.B. Suris. Variational symmetries and pluri-Lagrangian systems in classical mechanics. J. Nonlin. Math. Phys., 2017, 24, Sup. 1, p. 121-145. arXiv:1710.01526 [math-ph]

A.I. Bobenko, A. Sridhar, Abelian Higgs Vortices and Discrete Conformal maps, Lett. Mat. Phys. 108 (2018) 249-260 , Preprint (2017) arXiv:1703.04735 [math-ph]

M. Petrera, Yu.B. Suris. On the classification of multidimensionally consistent 3D maps. Lett. Math. Phys., 2017, 107, No. 11, p. 2013-2027. arXiv:1509.03129 [math-ph]

Yu.B. Suris, M. Vermeeren. On the Lagrangian structure of integrable hierarchies. - In: Advances in Discrete Differential Geometry, Ed. A.I. Bobenko, Springer, 2016, p. 347-378. Book on the Publisher's site. arXiv:1510.03724 [math-ph]

R. Boll, M. Petrera, Yu.B. Suris. On the variational interpretation of the discrete KP equation. - In: Advances in Discrete Differential Geometry, Ed. A.I. Bobenko, Springer, 2016, p. 379-405. Book on the Publisher's site. arXiv:1506.00729 [math-ph]

Yu.B. Suris. Variational symmetries and pluri-Lagrangian systems. - In: Dynamical Systems, Number Theory and Applications. A Festschrift in Honor of Armin Leutbecher's 80th Birthday, Eds. Th. Hagen, F. Rupp and J. Scheurle, World Scientific, 2016, p. 255-266. Book on the Publisher's site. arXiv:1307.2639 [math-ph]

R. Boll, M. Petrera, Yu.B. Suris. On integrability of discrete variational systems: octahedron relations. Internat. Math. Research Notices, 2016, 2016, No. 3, p. 645-668. arXiv:1406.0741 [nlin.SI]

A.I. Bobenko, A. Its, The asymptotic behaviour of the discrete holomorphic map Z^a via the Riemann-Hilbert method, Duke Math. J. 165:14, (2016), 2607-2682, Preprint (2014) arXiv:1409.2667 [math.CV]

A.I. Bobenko, W.K. Schief, Discrete line complexes and integrable evolution of minors, Proc. Royal Soc. A. 471, (2015) 20140819 ,DOI: 10.1098/rspa.2014.081, Preprint (2014) arXiv:1410.5794 [math.DG]

R. Boll, M. Petrera, Yu.B. Suris. Multi-time Lagrangian 1-forms for families of Bäcklund transformations. Relativistic Toda-type systems. J. Phys. A: Math. Theor., 2015, 48, No. 8, 085203, 28 pp. arXiv:1408.2405 [math-ph]

A.I. Bobenko, Yu.B. Suris. Discrete pluriharmonic functions as solutions of linear pluri-Lagrangian systems. Commun. Math. Phys., 2015, 336, No. 1, p. 199-215. arXiv:1403.2876 [math-ph]

R. Boll, M. Petrera, Yu.B. Suris. What is integrability of discrete variational systems? Proc. Royal Soc. A, 2014, 470, No. 2162, 20130550, 15 pp. arXiv:1307.0523 [math-ph]

R. Boll, M. Petrera, Yu.B. Suris. Multi-time Lagrangian 1-forms for families of Bäcklund transformations. Toda-type systems. J. Phys. A: Math. Theor., 2013, 46, No. 27, 275204, 26 pp. arXiv:1302.7144 [nlin.SI]

Yu.B. Suris. Variational formulation of commuting Hamiltonian flows: multi-time Lagrangian 1-forms. J. Geometric Mechanics, 2013, 5, No. 3, p. 365-379. arXiv:1212.3314 [math-ph]

R. Boll, Yu.B. Suris. On the Lagrangian structure of 3D consistent systems of asymmetric quad-equations. J. Phys. A: Math. Theor., 2012, 45, No. 11, 115201, 18 pp, arXiv:1108.0016 [nlin.SI]

V.E. Adler, A.I. Bobenko, Yu.B. Suris. Classification of integrable discrete equations of octahedron type. Internat. Math. Research Notices , 2012, 2012, 1822-1889, Preprint (2010) arXiv:1011.3527 [nlin.SI]

A.I. Bobenko, F. Günther, On discrete integrable equations with convex variational principles, Lett. Math. Phys. (2012), 102, 181-202, Preprint (2011) arXiv:1111.6273 [nlin.SI]

V.G. Papageorgiou, Yu.B. Suris, A.G. Tongas, A.P. Veselov. On quadrirational Yang-Baxter maps. SIGMA, 2010, 6, 033, 9 pp. arXiv:0911.2895 [math.QA]

A.I. Bobenko, Yu.B. Suris. On the Lagrangian structure of integrable quad-equations. Lett. Math. Phys., 2010, 92, No. 1, p. 17-31. arXiv:0912.2464 [nlin.SI]

R. Boll, Yu.B. Suris. Non-symmetric discrete Toda systems from quad-graphs. Applicable Analysis, 2010, 89, No. 4, p. 547-569. arXiv:0908.2822 [nlin.SI]

V.E. Adler, A.I. Bobenko, Yu.B. Suris. Integrable discrete nets in Grassmannians. Lett. Math. Phys., 2009, 89, No. 2, p. 131-139. arXiv:0812.5102 [math.DG]

[80]. V.E. Adler, A.I. Bobenko, Y.B. Suris, Discrete nonlinear hyperbolic equations. Classification of integrable cases, Functional Anal. and Appl. 43, No.1 (2009),  3-21, Preprint (2007) arXiv:0705.1663 [nlin.SI]  [pdf file](Russian)   [pdf file](English)