Zobrazeno 1 - 10
of 248
pro vyhledávání: '"Bobenko, Alexander"'
We define discrete constant mean curvature (cmc) surfaces in the three-dimensional Euclidean and Lorentz spaces in terms of sphere packings with orthogonally intersecting circles. These discrete cmc surfaces can be constructed from orthogonal ring pa
Externí odkaz:
http://arxiv.org/abs/2410.08915
Autor:
Bobenko, Alexander I.
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is a special
Externí odkaz:
http://arxiv.org/abs/2409.06573
We present a general approach for the study of dimer model limit shape problems via variational and integrable systems techniques. In particular we deduce the limit shape of the Aztec diamond and the hexagon for quasi-periodic weights through purely
Externí odkaz:
http://arxiv.org/abs/2407.19462
We study compact minimal surfaces in the 3-sphere which are constructed by successive reflections from a minimal $n$-gon -- so-called minimal reflection surfaces. The minimal $n$-gon solves a free boundary problem in a fundamental piece of the respec
Externí odkaz:
http://arxiv.org/abs/2406.12183
In this paper we develop a general approach to dimer models analogous to Krichever's scheme in the theory of integrable systems. We start with a Riemann surface and the simplest generic meromorphic functions on it and demonstrate how to obtain integr
Externí odkaz:
http://arxiv.org/abs/2402.08798
In 1883, Darboux gave a local classification of isothermic surfaces with one family of planar curvature lines using complex analytic methods. His choice of real reduction cannot contain tori. We classify isothermic tori with one family of planar curv
Externí odkaz:
http://arxiv.org/abs/2312.14956
The focus is on circular nets with one or two families of spherical parameter lines, which are treated in M\"obius geometry. These circular nets provide a discretisation of surfaces with one or two families of spherical curvature lines. The special c
Externí odkaz:
http://arxiv.org/abs/2312.04341
We introduce decorated piecewise hyperbolic and spherical surfaces and discuss their discrete conformal equivalence. A decoration is a choice of circle about each vertex of the surface. Our decorated surfaces are closely related to inversive distance
Externí odkaz:
http://arxiv.org/abs/2310.17529
We discuss a notion of discrete conformal equivalence for decorated piecewise euclidean surfaces (PE-surface), that is, PE-surfaces with a choice of circle about each vertex. It is closely related to inversive distance and hyperideal circle patterns.
Externí odkaz:
http://arxiv.org/abs/2305.10988