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Classification of Integrable Equations on Quad-Graphs. The Consistency Approach
Abstract: A classification of discrete integrable systems on quad–graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of theExpand
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Discrete isothermic surfaces.
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Discrete Differential Geometry: Integrable Structure
Classical differential geometry Discretization principles. Multidimensional nets Discretization principles. Nets in quadrics Special classes of discrete surfaces Approximation Consistency asExpand
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Discrete conformal maps and ideal hyperbolic polyhedra
We establish a connection between two previously unrelated topics: a particular discrete version of conformal geometry for triangulated surfaces, and the geometry of ideal polyhedra in hyperbolicExpand
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Surfaces in terms of 2 by 2 matrices
A test apparatus for the evaluation of the lubricity of rolling oils and the interaction of such oils with a variety of metal alloys employed in the construction of rolls. The axis of a driven workExpand
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A Discrete Laplace–Beltrami Operator for Simplicial Surfaces
TLDR
We define a discrete Laplace–Beltrami operator for simplicial surfaces based on the existence and uniqueness of Delaunay tessellations in piecewise flat surfaces. Expand
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Variational principles for circle patterns and Koebe’s theorem
We prove existence and uniqueness results for patterns of circles with prescribed intersection angles on constant curvature surfaces. Our method is based on two new functionals-one for the EuclideanExpand
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Integrable systems on quad-graphs
Discrete (lattice) systems constitute a well-established part of the theory of integrable systems. They came up already in the early days of the theory (see, e.g. [11, 12]), and took gradually moreExpand
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