TY - JOUR
T1 - An isoperimetric inequality in the universal cover of the punctured plane
AU - Alon, Noga
AU - Pinchasi, Adi
AU - Pinchasi, Rom
N1 - Funding Information:
We would like to thank Leonid Polterovich for introducing the problem to us and for many important comments. We also thank Misha Bialy for pointing out important references. Noga Alon’s research was supported in part by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University.
PY - 2008/12/6
Y1 - 2008/12/6
N2 - We find the largest ε{lunate} (approximately 1.71579) for which any simple closed path α in the universal cover over(R2 {set minus} Z2, ̃) of R2 {set minus} Z2, equipped with the natural lifted metric from the Euclidean two-dimensional plane, satisfies L (α) ≥ ε{lunate} A (α), where L (α) is the length of α and A (α) is the area enclosed by α. This generalizes a result of Schnell and Segura Gomis, and provides an alternative proof for the same isoperimetric inequality in R2 {set minus} Z2.
AB - We find the largest ε{lunate} (approximately 1.71579) for which any simple closed path α in the universal cover over(R2 {set minus} Z2, ̃) of R2 {set minus} Z2, equipped with the natural lifted metric from the Euclidean two-dimensional plane, satisfies L (α) ≥ ε{lunate} A (α), where L (α) is the length of α and A (α) is the area enclosed by α. This generalizes a result of Schnell and Segura Gomis, and provides an alternative proof for the same isoperimetric inequality in R2 {set minus} Z2.
KW - Isoperimetric inequality
KW - Universal covering space
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U2 - 10.1016/j.disc.2007.10.033
DO - 10.1016/j.disc.2007.10.033
M3 - Article
AN - SCOPUS:53049094586
SN - 0012-365X
VL - 308
SP - 5691
EP - 5701
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 23
ER -