2017/12/01 by Joseph Gordon, Gaiane Panina, Gordon, Joseph +3
Computer Science · Mathematics · #58K05 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1712.00299
openalex publication_date 2017/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe the configuration space \S of polygons with prescribed\nedge slopes, and study the perimeter \P as a Morse function on\n\S. We characterize critical points of \P (these are\n\tangential polygons) and compute their Morse indices. This setup is\nmotivated by a number of results about critical points and Morse indices of the\noriented area function defined on the configuration space of polygons with\nprescribed edge lengths (flexible polygons). As a by-product, we present an\nindependent computation of the Morse index of the area function (obtained\nearlier by G. Panina and A. Zhukova).\n