Discrete differential geometry. Consistency as integrability

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Bobenko, Alexander I.; Suris, Yuri B.;
(2005)
  • Subject: Nonlinear Sciences - Exactly Solvable and Integrable Systems | Mathematics - Complex Variables | Mathematics - Differential Geometry

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes ... View more
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    [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.

    [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.

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