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math.MG2025★ 1 cited
Quasi-symmetric nets: A constructive approach to the equimodular elliptic type of Kokotsakis polyhedra
A. Nurmatov, M. Skopenkov, F. Rist +2
A Kokotsakis polyhedron is a polyhedral mesh in three-dimensional Euclidean space formed by a central n-gonal face (the base), n quadrilateral faces each sharing one edge with the…
math.DG2025
Families of surfaces with constant ratio of principal curvatures and Plateau's problem
Mikhail Skopenkov, Khusrav Yorov
This work is on surfaces with a constant ratio of principal curvatures. These CRPC surfaces generalize minimal surfaces but are much more challenging to construct. We propose a con…
math.CO2025
Incidences, tilings, and fields
P. Pylyavskyy, M. Skopenkov
The master theorem, introduced by Richter-Gebert and generalized by Fomin and the first author, provides a method for proving incidence theorems of projective geometry using triang…