2022/08/09 by Anan'in, Sasha, Korshunov, Dmitrii
#Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2208.05076
We prove a conjecture of Ian Agol: all isometric realizations of a polyhedral surface with boundary sweep out an isotropic subset in the Kapovich-Millson moduli space of polygons isomorphic to the boundary. For a generic polyhedral disk we show that boundaries of its isometric realizations make up a Lagrangian subset. As an application of this result, we obtain a new solution to the problem of Richard Kenyon about spanning domes of piecewise linear curves comprised of unit intervals in R3.