We consider the configuration space of planar n-gons with fixed perimeter, which is diffeomorphic to the complex projective space CP n−2 . The oriented area function has the minimum number of critical points on the configuration space. We describe its critical points (these are regular stars) and compute their indices when they are Morse.
Translated title of the contributionКритические точки площади многоугольников с фиксированным периметром
Original languageEnglish
Pages (from-to)136-145
JournalЗАПИСКИ НАУЧНЫХ СЕМИНАРОВ САНКТ-ПЕТЕРБУРГСКОГО ОТДЕЛЕНИЯ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМ. В.А. СТЕКЛОВА РАН
Volume481
StatePublished - 2019

    Research areas

  • planar polygon, isoperimetric problems, configuration space, oriented area, critical point, Morse index

ID: 49857215