Standard

Polygons with prescribed edge slopes : configuration space and extremal points of perimeter. / Gordon, Joseph; Panina, Gaiane; Teplitskaya, Yana.

In: Beitrage zur Algebra und Geometrie, Vol. 60, No. 1, 12.03.2019, p. 1-15.

Research output: Contribution to journal › Article › peer-review

Harvard

Gordon, J, Panina, G & Teplitskaya, Y 2019, 'Polygons with prescribed edge slopes: configuration space and extremal points of perimeter', Beitrage zur Algebra und Geometrie, vol. 60, no. 1, pp. 1-15. https://doi.org/10.1007/s13366-018-0409-3, https://doi.org/10.1007/s13366-018-0409-3

APA

Gordon, J., Panina, G., & Teplitskaya, Y. (2019). Polygons with prescribed edge slopes: configuration space and extremal points of perimeter. Beitrage zur Algebra und Geometrie, 60(1), 1-15. https://doi.org/10.1007/s13366-018-0409-3, https://doi.org/10.1007/s13366-018-0409-3

Vancouver

Gordon J, Panina G, Teplitskaya Y. Polygons with prescribed edge slopes: configuration space and extremal points of perimeter. Beitrage zur Algebra und Geometrie. 2019 Mar 12;60(1):1-15. https://doi.org/10.1007/s13366-018-0409-3, https://doi.org/10.1007/s13366-018-0409-3

Author

Gordon, Joseph ; Panina, Gaiane ; Teplitskaya, Yana. / Polygons with prescribed edge slopes : configuration space and extremal points of perimeter. In: Beitrage zur Algebra und Geometrie. 2019 ; Vol. 60, No. 1. pp. 1-15.

BibTeX

@article{6d9e85b5e3b14e929872d01c5cbac1b2,
title = "Polygons with prescribed edge slopes: configuration space and extremal points of perimeter",
abstract = "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).",
keywords = "Индекс Морса, функция Ботта-Морса, конфигурационное пространство",
author = "Joseph Gordon and Gaiane Panina and Yana Teplitskaya",
year = "2019",
month = mar,
day = "12",
doi = "10.1007/s13366-018-0409-3",
language = "English",
volume = "60",
pages = "1--15",
journal = "Beitrage zur Algebra und Geometrie",
issn = "0138-4821",
publisher = "Springer Nature",
number = "1",

}

RIS

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 - 2019/3/12

Y1 - 2019/3/12

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).

KW - Индекс Морса, функция Ботта-Морса, конфигурационное пространство

UR - http://www.scopus.com/inward/record.url?scp=85061922782&partnerID=8YFLogxK

U2 - 10.1007/s13366-018-0409-3

DO - 10.1007/s13366-018-0409-3

M3 - Article

AN - SCOPUS:85061922782

VL - 60

SP - 1

EP - 15

JO - Beitrage zur Algebra und Geometrie

JF - Beitrage zur Algebra und Geometrie

SN - 0138-4821

IS - 1

ER -

ID: 32594706