3 papers
math.DS2026
Integrability of Cauchy problems for discrete conformal maps and circle patterns
Maxim Arnold, Anton Izosimov
A map from a square lattice to the Riemann sphere is called discrete conformal if the image of every elementary square is a harmonic quadrilateral. We prove that the initial value…
math.DS2024
A family of maps and a vector field on plane polygons
Maxim Arnold, Lael Costa, Serge Tabachnikov
We study, theoretically and experimentally, a 1-parameter family of transformations and their limiting vector field on the space of plane polygons. These transformations are discre…
math.DG2023
Symmedians as Hyperbolic Barycenters
Maxim Arnold, Carlos E. Arreche
The symmedian point of a triangle enjoys several geometric and optimality properties, which also serve to define it. We develop a new dynamical coordinatization of the symmedian, w…