An emerging field of discrete differential geometry aims at the development of discrete
equivalents of notions and methods of classical differential geometry. The latter appears as …

A classification of discrete integrable systems on quad–graphs, ie on surface cell
decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis …

An introduction, at a basic level, to the conformal differential geometry of surfaces and
submanifolds is given. That is, the book discusses those aspects of the geometry of surfaces …

Discrete differential geometry aims to develop discrete equivalents of the geometric notions
and methods of classical differential geometry. This survey contains a discussion of the …

Long before the theory of solitons, geometers used integrable equations to describe various
special curves and surfaces. Nowadays this field of research takes advantage of using both …

Motivated by the classical studies on transformations of conjugate nets, we develop the
general geometric theory of transformations of their discrete analogs: the multidimensional …

Circular meshes are quadrilateral meshes all of whose faces possess a circumcircle,
whereas conical meshes are planar quadrilateral meshes where the faces which meet in a …

It is shown that the discrete Darboux system, descriptive of conjugate lattices in Euclidean
spaces, admits constraints on the (adjoint) eigenfunctions which may be interpreted as …

We study the Desargues maps, which generate lattices whose points are collinear with all
their nearest (in positive directions) neighbours. The multi-dimensional compatibility of the …

Affine spheres with definite and indefinite Blaschke metric are discretized in a purely
geometric manner. The technique is based on simple relations between affine spheres and …