3 papers
math.MG2025
Flexible polyhedral nets in isotropic geometry
O. Pirahmad, H. Pottmann, M. Skopenkov
We study flexible polyhedral nets in isotropic geometry. This geometry has a degenerate metric, but there is a natural notion of flexibility. We study infinitesimal and finite flex…
math-ph2024
Feynman checkers: through the looking-glass
Fedor Ozhegov, Mikhail Skopenkov, Alexey Ustinov
Feynman gave a famous elementary introduction to quantum theory by discussing the thin-film reflection of light. We make his discussion mathematically rigorous, keeping it elementa…
math.MG2024
Area preserving Combescure transformations
O. Pirahmad, H. Pottmann, M. Skopenkov
Motivated by the design of flexible nets, we classify all nets of arbitrary size m x n that admit a continuous family of area-preserving Combescure transformations. There are just…