# Discrete differential geometry. Consistency as integrability

- Published: 18 Apr 2005

M. Berger. Geometry. Berlin etc.: Springer-Verlag, 1987.

L. Bianchi. Lezioni di geometria differenziale. 3rd edition. Pisa: Enrico Spoerri, 1923 (Italian). iv+806, xi+832 pp.

W. Blaschke. Projektive Geometrie. 3rd edition. Basel etc.: Birkh¨auser, 1954. 197 pp.

Thomsen. Berlin: Springer, 1929 (German). x+474 pp.

A.I. Bobenko. Discrete conformal maps and surfaces. - In: SIDE III - Symmetries and integrability of difference equations (Sabaudia, 1998), CRM Proc. Lecture Notes, 225 (2000), pp.

A.I. Bobenko, U. Hertrich-Jeromin. Orthogonal nets and Clifford algebras. Toˆhoku Math. Publ. 20 (2001), 7-22.

[BobHoSp] A.I. Bobenko, T. Hoffmann, B.A. Springborn. Discrete minimal surfaces: geometry from combinatorics. Annals of Math., 2005 (to appear).

[BobHoSu] 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. Int. Math. Res. Not. 2002, no. 3, 111-164. [OpenAIRE]

[BobMaS1] A.I. Bobenko, D. Matthes, Yu.B. Suris. Nonlinear hyperbolic equations in surface theory: integrable discretizations and approximation results. Algebra Anal., 2005 (to appear).

[BobMaS2] A.I. Bobenko, D. Matthes, Yu.B. Suris. Discrete and smooth orthogonal systems: C∞-approximation. Int. Math. Res. Not., 45 (2003), 2415-2459. [OpenAIRE]

[BobMeS] 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 Angew. Math., 2005 (to appear).

A.I. Bobenko, U. Pinkall. Discrete surfaces with constant negative Gaussian curvature and the Hirota equation. J. Differential Geom., 43 (1996), no. 3, 527-611. [OpenAIRE]

A.I. Bobenko, U. Pinkall. Discrete isothermic surfaces. J. Reine Angew. Math., 475 (1996), 187-208. [OpenAIRE]

A.I. Bobenko, U. Pinkall. Discretization of surfaces and integrable systems. - In: Discrete integrable geometry and physics, Eds. A.I. Bobenko and R. Seiler, Oxford: Clarendon Press, 1999, pp. 3-58. [OpenAIRE]

[BobSch1] A.I. Bobenko, W.K. Schief. Discrete indefinite affine spheres. - In: Discrete integrable geometry and physics, Eds. A.I. Bobenko and R. Seiler, Oxford: Clarendon Press, 1999, pp. 113-138.