Alexander Bobenko, Ulrich Pinkall, Boris Springborn, Discrete conformal maps and ideal hyperbolic polyhedra, Preprint (2010) arXiv:1005.2698 [math.GT]
A.I. Bobenko, Yu.B. Suris, On the Lagrangian structure of integrable quad-equations, Lett. Math. Phys. 92, No.1 (2010), 17-31, Preprint (2009) arXiv:0912.2464 [nlin.SI]
A.I. Bobenko, Ch. Mercat, M. Schmies, Conformal Structures and Period Matrices of Polyhedral Surfaces, Preprint (2009) arXiv:0909.1305 [math.DG]
A.I. Bobenko, H. Pottmann, J. Wallner, A curvature theory for discrete surfaces based on mesh parallelity, Math. Annalen (to appear), Preprint (2009) arXiv:0901.4620 [math.DG]
V.E. Adler, A.I. Bobenko, Yu.B. Suris, Integrable discrete nets in Grassmannians, Lett. Math. Phys. 89 (2009) 131-139, Preprint (2008) arXiv:0812.5102 [math.DG]
Alexander I. Bobenko, Yuri B. Suris,
Discrete Differential Geometry: Integrable Structure, Graduate Studies in
Mathematics, Vol. 98, AMS, 2008, xxiv + 404 p
ISBN-10: 0-8218-4700-7
ISBN-13: 978-0-8218-4700-8
A.I. Bobenko, P. Schröder, J.M. Sullivan, G.M. Ziegler (Eds.), Discrete Differential Geometry, Series: Oberwolfach Seminars, Vol. 38, Birkhäuser, Basel, 2008, X+341 p.
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]
A.I. Bobenko, S.P. Tsarev, Curvature line parametrization from circle patterns (2007) arXiv:0706.3221 [math.DG]
M. Fischer, B. Springborn, P. Schröder, A.I. Bobenko, An Algorithm for the Construction of Intrinsic Delaunay Triangulations with Applications to Digital Geometry Processing, Computing 81:2-3 (2007) 199-213, Preprint (2006)
A.I. Bobenko, Surfaces from Circles, In: Discrete Differential Geometry, A.I. Bobenko, P. Schröder, J.M. Sullivan, G.M. Ziegler, (eds.), Series: Oberwolfach Seminars, Vol. 38, 2008, (Preprint) arXiv:0707.1318 [math.DG]
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]
H. Pottmann, Y. Liu, J. Wallner, A. Bobenko, W. Wang, Geometry of Multi-layer Freeform Structures for Architecture, ACM Trans. Graphics 26(3) (2007), SIGGRAPH 2007
A.I. Bobenko, Yu.B. Suris, Isothermic surfaces in sphere geometries as Moutard nets, Proc. Royal. Soc. A. 463 (2007) 3171-3193, Preprint (2006) math.DG/0610434
A.I. Bobenko, I. Izmestiev, Alexandrov's theorem, weighted Delaunay triangulations, and mixed volumes, Annales de l'Institut Fourier 58:2 (2008) 447-505, Preprint (2006) math.DG/0609447
A.I. Bobenko, Yu.B. Suris, On organizing principles of Discrete Differential Geometry. Geometry of spheres. Russian Math. Surveys, 62:1 (2007) 1-43, Preprint (2006) math.DG/0608291
A.I. Bobenko, Yu.B. Suris, Discrete differential geometry. Consistency as integrability, Preliminary version of a book (2005) math.DG/0504358
A.I. Bobenko, P. Schröder, Discrete Willmore Flow, Eurographics Symposium on Geometry Processing (2005), M. Desbrun, H. Pottmann (eds.), 101-110
A.I. Bobenko, B.A. Springborn, A discrete Laplace-Beltrami operator for simplicial surfaces, Discrete and Computational Geometry 38:4 (2007) 740-756, Preprint (2005) math.DG/0503219
A.I. Bobenko, A conformal energy for simplicial surfaces, Combinatorial and Computational Geometry, MSRI Publications, V. 52, 2005, 133-143, Preprint (2004) math.DG/0406128
A.I. Bobenko, Ch. Mercat, Yu.B. Suris, Linear and nonlinear theories of discrete analytic functions. Integrable structure and isomonodromic Green's function, J. reine und angew. Math. 583 (2005) 117-161 math.DG/0402097
A.I. Bobenko, Geometry of discrete integrability. The consistency approach, In: Faddeev et al. (eds.), Bilinear Integrable Systems: From Classical to Quantum, Continous to Discrete, 2006, Springer, 43-53
A.I. Bobenko, Discrete Differential Geometry. Integrability as Consistency. In: Lect. Notes Phys. 644, 85-110 (2004)
V.E. Adler, A.I. Bobenko, Yu.B. Suris, Geometry of Yang-Baxter maps: pencils of conics and quadrirational mappings, Communications in Analysis and Geometry 12:5 (2004) 967-1008 math.QA/0307009
A.I. Bobenko, T. Hoffmann, B.A. Springborn, Minimal surfaces from circle patterns: Geometry from combinatorics, Ann. of Math. 164:1 (2006) 231-264, Preprint (2003) math.DG/0305184
A.I. Bobenko, D. Matthes, Yu.B. Suris, Discrete and smooth orthogonal systems: $C^\infty$-approximation, Internat. Math. Research Notices 2003:45, 2415-2459 Preprint (2003) math.DG/0303333
S.I. Agafonov, A.I. Bobenko, Hexagonal circle patterns with constant intersection angles and discrete Painleve and Riccati equations, J. Math. Phys. 44:8 (2003) 3455-3469, Preprint (2003) math.CV/0301282
A.I. Bobenko, D. Matthes, Yu.B. Suris, Nonlinear hyperbolic equations in surface theory: integrable discretizations and approximation results, Algebra and Analysis 17:1 (2005) 53-83, St. Petersburg Math. J. 17:1 (2206), 39-61 math.NA/0208042
A.I. Bobenko, Yu.B. Suris, Integrable non-commutative equations on quad-graphs. The consistency approach, Lett. Math. Phys. 61 (2002) 241-254, SFB288 Preprint 558 (2002) nlin.SI/0206010
B.Deconinck, M. Heil, A.I. Bobenko, M. van Hoeij, M. Schmies, Computing Riemann Theta Functions, Mathematics of Computation 73 (2004) 1417-1442, SFB288 Preprint 560 (2002) nlin.SI/0206009
A.I. Bobenko, T.V. Pavlyukevich, B.A. Springborn, Hyperbolic constant mean curvature one surfaces: Spinor representation and trinoids in hypergeometric functions, Math. Z. 245 (2003) 63-91, SFB288 Preprint 554 (2002) math.DG/0206021
A.I. Bobenko, B.A. Springborn, Variational principles for circle patterns and Koebe's theorem, Trans. AMS 356 (2004) 659-689, SFB288 Preprint 545 (2002), arXiv:math/0203250
V. E. Adler, A.I. Bobenko, Yu.B. Suris, Classification of integrable equations on quad-graphs. The consistency approach, Comm. Math. Phys. 233 (2003) 513-543 SFB288 Preprint 557 (2002), nlin.SI/0202024
A.I. Bobenko, Yu.B. Suris, Integrable systems on quad-graphs, International Math. Research Notices 2002:11, 573-612, SFB288 Preprint 521 (2001) nlin.SI/0110004
A.I. Bobenko, T. Hoffmann, Hexagonal circle patterns and integrable systems. Patterns with constant angles, Duke Math. J. 116:3 (2003) 525-566 SFB288 Preprint 516 (2001) math.CV/0109018
A.I. Bobenko, T. Hoffmann, Yu.B. Suris, Hexagonal circle patterns and integrable systems. Patterns with the multi-ratio property and Lax equations on the regular triangular lattice, International Math. Research Notices 2002:3, 111-164 SFB288 Preprint 502 (2001) math.CV/0104244
A.I. Bobenko, M. Umehara, Monodromy of isometric deformations of CMC surfaces, Hiroshima Math. Journal 31:2 (2001) 291-297
A.I. Bobenko, T. Hoffmann, Conformally symmetric circle packings. A generalization of Doyle spirals, Experimental Mathematics 10:1 (2001) 141-150 SFB288 Preprint 468 (2000), interactive version with Java applets, math.CV/0005245
A.I. Bobenko, U. Eitner, Painlevé Equations in the Differential Geometry of Surfaces, Lecture Notes in Mathematics, 1753, Springer, Berlin, 2000, VI+120 p.
A.I. Bobenko, Yu.B. Suris, A Discrete Time Lagrange Top and Discrete Elastic Curves, Amer. Math. Soc. Transl. (2) 201 (2000) 39-62
S.I. Agafonov, A.I. Bobenko, Discrete Z^a and Painleve Equations, International Math. Research Notices 2000:4 165-193, SFB288 Preprint 404 (1999), solv-int/9909002
A.I. Bobenko, Exploring Surfaces through Methods from the Theory of Integrable Systems: The Bonnet Problem, In: Surveys on Geometry and Integrable Systems, Advanced Studies in Pure Mathematics 51 (2008) 1-51, SFB288 Preprint 403 (1999), math.DG/9909003
A.I. Bobenko, Yu.B. Suris, Discrete Lagrangian Reduction, Discrete Euler-Poincaré Equations, and Semidirect Products, Lett. Math. Phys. 49 (1999) 79-93, SFB288 Preprint 398, math.SG/9906108
A.I. Bobenko, Yu.B. Suris, Discrete time Lagrangian mechanics on Lie groups, with an application on the Lagrange top, Comm. Math. Phys. 204 (1999), 147-188, SFB288 Preprint 345 (1998), solv-int/9810018
Book. Discrete Integrable Geometry and Physics, eds. A.I. Bobenko, R. Seiler, Clarendon Press, Oxford, 1999, XIII+370 [For content and introduction see SFB288 Preprint 325]
A.I. Bobenko, A.V. Kitaev, On Asymptotic Cones of Surfaces with Constant Curvature and the Third Painleve Equation, Manuscripta Math. 97 (1998), 489-516 SFB288 Preprint 315 (1998)
A.I. Bobenko, B. Lorbeer, Yu.B. Suris, Integrable Discretizations of the Euler top, Journal of Mathematical Physics, Vol. 39:12 (1998), 6668-6683 SFB288 Preprint 312 (1998), solv-int/9803016
A.I. Bobenko, U.J. Hertrich-Jeromin, Orthogonal Nets and Clifford Algebras, Tohoku Math. Publ. 20 (2001) 7-22, SFB288 Preprint 310 (1998), math.DG/9802126
A.I. Bobenko, Discrete Integrable Systems and Geometry, In: "12th International Congress of mathematical Physics ICMP '97", (Brisbane, Australia, July 1997) Eds. D. De Wit, A.J. Bracken, M.D. Gould, P.A. Pearce, International Press, Boston 1999, pp. 219-226, SFB288 Preprint 298 (1997)
A.I. Bobenko, W.K. Schief, Affine Spheres: Discretization via Duality Relations, Experimental Mathematics 8:3 (1999), 261-280 SFB288 Preprint 297 (1997)
A.I. Bobenko, U. Pinkall, Discretization of Surfaces and Integrable Systems, In: A.I. Bobenko, R. Seiler (eds.) "Discrete Integrable Geometry and Physics", Oxford University Press (1999) pp. 3-58 SFB288 Preprint 296 (1997)
A.I. Bobenko, Helicoids with Handles and Baker-Akhiezer Spinors, Math. Z. 229 (1998), 9-29 SFB288 Preprint 264 (1997)
A.I. Bobenko, W.K. Schief, Discrete Indefinite Affine Spheres, In: A.I. Bobenko, R. Seiler (eds.) "Discrete Integrable Geometry and Physics", Oxford University Press (1999) pp.113-138 SFB288 Preprint 263 (1997)
A.I. Bobenko, Discrete Conformal Maps and Surfaces, In: P.A. Clarkson, F.W. Nijhoff (eds.) "Symmetries and Integrability of Difference Equations", London Mathematical Society Lecture Notes Series 255, Cambridge University Press 1999, pp. 97- 108 (GANG Preprint IV.27 , University of Massachusetts, Amherst (1996))
A.I. Bobenko, U. Eitner, A.V. Kitaev, Harmonic Inverse Mean Curvature Surfaces and Painleve Equations, Geometriae Dedicata 68 (1997) 187-227 SFB288 Preprint 182 (1995)
V. Bazhanov, A. Bobenko, N. Reshetikhin, Quantum Discrete Sine-Gordon Model at Roots of 1: Integrable Quantum System on the Integrable Classical Background, Comm. Math. Phys. 175 (1996) 377-400 SFB288 Preprint 166 (1995)
A.I. Bobenko, U. Eitner, Bonnet Surfaces and Painleve Equations, J. reine angew. Math. 499 (1998) 47-79 SFB288 Preprint 151 (1994)
A.I. Bobenko, U. Pinkall, Discrete Isothermic Surfaces, J. reine angew. Math. 475 (1996) 187-208 SFB288 Preprint 143 (1994)
A.I. Bobenko, U. Pinkall, Discrete Surfaces with Constant Negative Gaussian Curvature and the Hirota Equation, J. Differential Geometry 43 (1996) 527-611, SFB288 Preprint 127 (1993)
A.I. Bobenko, Surfaces in Terms of 2 by 2 Matrices. Old and New Integrable Cases, SFB288 Preprint 66 (1993) In: A.P. Fordy, J.C. Wood (eds.) "Harmonic Maps and Integrable Systems", Vieweg, Braunschweig/Wiesbaden 1994, pp. 81-127
A.I. Bobenko, N. Ercolani, H. Knoerrer, E. Trubowitz, Density of heat curves in the moduli space, Panoramas of Mathematics, Banach Center Publications, v. 34, 19-27, Warszava (1995)
A.I. Bobenko, A.R. Its A, The Painlevé III Equation and the Iwasawa Decomposition, Manuscripta Mathematica 87, 369-377 (1995)
A.I. Bobenko, S.B. Kuksin, The Nonlinear Klein-Gordon Equation on an Interval as a Perturbed Sine-Gordon Equation, Comm. Math. Helvetici 70, 63-112 (1995)
A.I. Bobenko, S.B Kuksin, Small-Amplitude Solutions of the Sine-Gordon Equation on an Interval under Dirichlet or Neumann Boundary Conditions, Journal of Nonlinear Science 5, 207-232 (1995)
E.D. Belokolos, A.I. Bobenko, V.Z. Enolski, A.R. Its, V.B. Matveev, "Algebro-geometric approach in the theory of integrable equations", Springer Series in Nonlinear Dynamics, Springer, Berlin, 1994, XII+337 p.
M.V. Babich, A.I. Bobenko, Willmore tori with umbilic lines and minimal surfaces in hyperbolic space, Duke Mathematical Journal 72:1, 151-185 (1993)
A.I. Bobenko, M. Bordemann, C. Gunn, U. Pinkall, On two integrable cellular automata, Comm. Math. Phys. 158, 127-134 (1993)
A.I. Bobenko, N. Kutz, U. Pinkall, The discrete quantum pendulum, Physics Letters A 177, 399-404 (1993)
A.I. Bobenko, Integrable surfaces. In "Nonlinear World" (ed. V.G.Bar´yakhtar et al.), v.1, 36-55, World Scientific, Singapore (1990)
A.I. Bobenko, Integrable surfaces. Functional Anal. i Priloz. 24:3, 68-69 (1990), [Functional Anal. Appl. 24, 227-228 (1991)]
A.I. Bobenko, All constant mean curvature tori in R3, S3 and H3 in terms of theta-functions. Math. Ann. 290, 209-245 (1991)
A.I. Bobenko, S.B. Kuksin, Finite-gap solutions of the KdV equation are non-degenerate. Physics Letters A 161, 274-276 (1991)
A.I. Bobenko, Constant mean curvature surfaces and integrable equations. Uspekhi Mat. Nauk 46:4, 3-42 (1991), [English transl.: Russian Math. Surveys 46:4, 1-45 (1991)]
A.I. Bobenko, A.G. Reyman, M.A. Semenov-Tian-Shansky, The Kowalewski top 99 years later: a Lax pair, generalizations and explicit solutions. Comm. Math. Phys. 122, 321-354 (1989)
A.I. Bobenko, L.A. Bordag, Periodic multiphase solutions of the Kadomsev-Petviashvili equation. J. Phys. A: Math. Gen. 22, 1259-1274 (1989)
A.I. Bobenko, Eigenfunctions of the Dirichlet and Neumann problems for the elliptic sinh-Gordon equation on a rectangle. Zap. Nauch. Semin. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 179, 32-36 (1989), [translated in J. Soviet Math.]
A.I. Bobenko, Finite-gap constant mean curvature tori in R3 and S3. LOMI preprint E-3-89, Leningrad (1989)
A.I. Bobenko, V.B Kuznetsov, Lax representation and new formulae for the Goryachev-Chaplygin top. J. Phys. A: Math. Gen. 21, 1999-2006 (1988)
A.I. Bobenko, Schottky uniformization and finite-gap integration. Dokl. Akad. Nauk SSSR, 295:2, 268-272 (1987), [Soviet Math. Dokl. 36:1, 38-42 (1988)]
A.I. Bobenko, L.A. Bordag, Qualitative analysis of finite-gap solutions of the KdV equation by the automorphic approach. Zap. Nauch. Semin. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 165, 31-41 (1987), [J.Soviet Math. 50:6, 1951-1959 (1990)]
A.I. Bobenko, D.A. Kubensky, Qualitative analysis and calculations of the finite-gap solutions of the KdV equation. An automorphic approach. Teor. Mat. Fiz. 72:3, 352-360 (1987), [ Theor. Math. Phys. 72:3, 929-935, (1987) ]
M.V. Babich, A.I. Bobenko, V.B. Matveev, Solutions of nonlinear equations integrable
in Jacobi theta functions by the method of the inverse problem and symmetries
of algebraic curves. Izvestiya Akad. Nauk SSSR, ser. Math., 49:3,
511-529 (1985), [Math. USSR Izvestiya, 26:3, 479-496 (1986)]
A.I. Bobenko, Euler´s equations on algebras e(3) and so(4). Isomorphism of integrable cases. Functional Anal. i Priloz. 20:1, 64-66 (1986), [Functional Anal. Appl. 20, 53-56 (1986)]
E.D. Belokolos, A.I. Bobenko, V.Z. Enolskii, V.B. Matveev, Algebro-geometric principles of superposition of finite-zone solutions of integrable non-linear equations. Uspekhi Mat. Nauk 41:2, 3-42 (1986), [Russian Math. Surveys 41:2, 1-49 (1986)]
A.I. Bobenko, Uniformization and finite-gap integration. LOMI preprint P-10-86, Leningrad (1986) [in Russian]
A.I. Bobenko, Real algebro-geometric solutions of the Landau-Lifshitz equation by Prym theta-functions. Functional Anal. i Priloz. 19:1, 6-19 (1985), [Functional Anal. Appl. 19, 5-17 (1985)]
R.F. Bikbaev, A.I. Bobenko, A.R. Its, The Landau-Lifshitz equation. The theory of solutions I and II. Preprints Don FTI-84-6(81) and FTI-84-7(82), Donetsk (1984) [in Russian]
A.I. Bobenko, On periodic finite-zone solutions of the sine-Gordon equation. Functional Anal. i Priloz. 18:3, 74-75 (1984), [Functional Anal. Appl. 18, 240-242 (1984)]
A.I. Bobenko, Darboux transformation and rational solutions of the rank 2 of the Kadomsev-Petviashvili equation. Vestnik Leningrad Univ. 22, 74-77 (1984) [in Russian]
A.I. Bobenko, Landau-Lifshitz equation. Dressing up of the solutions and the elementary excitations. Zap. Nauch. Semin. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 123, 58-66 (1983), [J.Soviet Math. 28:4, 499-505 (1985)]
A.I. Bobenko, Finite-range solutions in the language of automorphic finctions. The Kadomsev-Petviashvili equation. Zap. Nauch. Semin. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 129, 5-16 (1983), [J.Soviet Math. 29:2, 1101-1110 (1985)]
M.V. Babich, A.I. Bobenko, V.B. Matveev, Reduction of Riemann theta-functionsof genus g to theta-functions of lower genus and symmetries of algebraic curves. Dokl. Akad. Nauk SSSR, 272:1, 13-17 (1983), [Soviet Math. Dokl. 28, 304-308 (1983)]
R.F. Bikbaev, A.I. Bobenko, A.R. Its, Finite-zone integration of the Landau-Lifshitz equation. Dokl. Akad. Nauk SSSR, 272:6, 1293-1298 (1983), [Soviet Math. Dokl. 28, 512-516 (1983)]
A.I. Bobenko, V.B. Matveev, M.A. Salle, Nonlocal equations of Korteweg-de Vries and Kadomsev-Petviashvili. Dokl. Akad. Nauk SSSR 265:6, 1357-1360 (1982), [English transl.: Soviet Phys. Dokl. 27, 610-611 (1982)]