On Some Isoperimetric Inequality In The Universal Covering Space Of The Punctured Plane
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چکیده
We find the largest ǫ for which any simple closed path α in the universal cover R̃2 \ Z2 of R2 \ Z2, equipped with the natural lifted metric from the Euclidean two dimensional plane, satisfies L(α) ≥ ǫA(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 Gomis, and provides an alternative proof for the same isoperimetric inequality in R2 \ Z2
منابع مشابه
An isoperimetric inequality in the universal cover of the punctured plane
Discrete Mathematics xx (xxxx) xxx–xxx Abstract 3 We find the largest (approximately 1.71579) for which any simple closed path α in the universal cover R 2 \ Z 2 of R 2 \ Z 2 , 4 equipped with the natural lifted metric from the Euclidean two-dimensional plane, satisfies L(α) ≥ A(α), where L(α) is the 5 length of α and A(α) is the area enclosed by α. This generalizes a result of Schnell and Segu...
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تاریخ انتشار 2009