Geodesic
Oriented area as a Morse function on polygon spaces
Ars Mathematica Contemporanea, Tome 19 (2020) no. 1, pp. 155-171.

Voir la notice de l'article provenant de la source Ars Mathematica Contemporanea website

We study polygon spaces arising from planar configurations of necklaces with some of the beads fixed and some of the beads sliding freely. These spaces include configuration spaces of flexible polygons and some other natural polygon spaces. We characterise critical points of the oriented area function in geometric terms and give a formula for the Morse indices. Thus we obtain a generalisation of isoperimetric theorems for polygons in the plane.
DOI : 10.26493/1855-3974.2286.ece
Keywords: Flexible polygons, configuration spaces, Morse index, critical points 
@article{10_26493_1855_3974_2286_ece,
     author = {Daniil Mamaev},
     title = {Oriented area as a {Morse} function on polygon spaces},
     journal = {Ars Mathematica Contemporanea},
     pages = {155--171},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2020},
     doi = {10.26493/1855-3974.2286.ece},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2286.ece/}
}
TY  - JOUR
AU  - Daniil Mamaev
TI  - Oriented area as a Morse function on polygon spaces
JO  - Ars Mathematica Contemporanea
PY  - 2020
SP  - 155
EP  - 171
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2286.ece/
DO  - 10.26493/1855-3974.2286.ece
LA  - en
ID  - 10_26493_1855_3974_2286_ece
ER  - 
%0 Journal Article
%A Daniil Mamaev
%T Oriented area as a Morse function on polygon spaces
%J Ars Mathematica Contemporanea
%D 2020
%P 155-171
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2286.ece/
%R 10.26493/1855-3974.2286.ece
%G en
%F 10_26493_1855_3974_2286_ece
Daniil Mamaev. Oriented area as a Morse function on polygon spaces. Ars Mathematica Contemporanea, Tome 19 (2020) no. 1, pp. 155-171. doi : 10.26493/1855-3974.2286.ece. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2286.ece/

Cité par Sources :