Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4649974 | Discrete Mathematics | 2008 | 11 Pages |
Abstract
We find the largest ϵϵ (approximately 1.71579) for which any simple closed path αα in the universal cover R2∖Z2˜ of R2∖Z2R2∖Z2, equipped with the natural lifted metric from the Euclidean two-dimensional plane, satisfies L(α)≥ϵA(α)L(α)≥ϵA(α), where L(α)L(α) is the length of αα and A(α)A(α) is the area enclosed by αα. This generalizes a result of Schnell and Segura Gomis, and provides an alternative proof for the same isoperimetric inequality in R2∖Z2R2∖Z2.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Noga Alon, Adi Pinchasi, Rom Pinchasi,