TY - JOUR
T1 - Polygons with prescribed edge slopes
T2 - configuration space and extremal points of perimeter
AU - Gordon, Joseph
AU - Panina, Gaiane
AU - Teplitskaya, Yana
PY - 2019/3/6
Y1 - 2019/3/6
N2 - We describe the configuration space S of polygons with prescribed edge slopes, and study the perimeter P as a Morse function on S. We characterize critical points of P (these are tangential polygons) and compute their Morse indices. This setup is motivated by a number of results about critical points and Morse indices of the oriented area function defined on the configuration space of polygons with prescribed edge lengths (flexible polygons). As a by-product, we present an independent computation of the Morse index of the area function (obtained earlier by Panina and Zhukova).
AB - We describe the configuration space S of polygons with prescribed edge slopes, and study the perimeter P as a Morse function on S. We characterize critical points of P (these are tangential polygons) and compute their Morse indices. This setup is motivated by a number of results about critical points and Morse indices of the oriented area function defined on the configuration space of polygons with prescribed edge lengths (flexible polygons). As a by-product, we present an independent computation of the Morse index of the area function (obtained earlier by Panina and Zhukova).
U2 - 10.1007/s13366-018-0409-3
DO - 10.1007/s13366-018-0409-3
M3 - Article
SN - 2191-0383
VL - 60
SP - 1
EP - 15
JO - Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
JF - Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
ER -