An isoperimetric inequality in the universal cover of the punctured plane

We find the largest for which any simple closed path in the universal cover R2 \ Z2 of R2 \ Z2, equipped with the natural lifted metric from the Euclidean two dimensional plane, satisfies L() A(), where L() is the length of and A() is the area enclosed by . This generalizes a result of Schnell and Segura Gomis, and provides an alternative proof for the same isoperimetric inequality in R2 \ Z2

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Noga Alon, Adi Pinchasi, Rom Pinchasi
• Keywords: Dimensional Plane, DM 2008, Simple Closed Path, Universal Cover