 
Summary: UNCORRECTED
PROOF
DISC: 7262 + Model pp. 111 (col. fig: NIL)
ARTICLE IN PRESS
Discrete Mathematics xx (xxxx) xxxxxx
www.elsevier.com/locate/disc
An isoperimetric inequality in the universal cover of the punctured
plane
Noga Alona, Adi Pinchasia, Rom Pinchasib
a Schools of Mathematics and Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences,
Tel Aviv University, Tel Aviv 69978, Israel
b Mathematics Department, TechnionIsrael Institute of Technology, Haifa 32000, Israel
Received 29 May 2007; received in revised form 16 October 2007; accepted 25 October 2007
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2
Abstract 3
We find the largest (approximately 1.71579) for which any simple closed path in the universal cover R2 \ Z2 of R2 \ Z2, 4
equipped with the natural lifted metric from the Euclidean twodimensional plane, satisfies L() A(), where L() is the 5
length of and A() is the area enclosed by . This generalizes a result of Schnell and Segura Gomis, and provides an alternative 6
proof for the same isoperimetric inequality in R2 \ Z2. Q1 7
