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Browsing Mathematics by Author "Valdivia, Aaron D."
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Item Asymptotic Translation Length in the Curve Complex(New York Journal of Mathematics, 2013) Valdivia, Aaron D.We show that when the genus and punctures of a surface are directly proportional by some rational number the minimal asymptotic translation length in the curve complex has behavior inverse to the square of the Euler characteristic. We also show that when the genus is fixed and the number of punctures varies the behavior is inverse to the Euler characteristic.Item Lipschitz Constants To Curve Complexes For Punctured Surfaces(Elsevier B.V, 2014) Valdivia, Aaron D.We give asymptotic bounds for the optimal Lipschitz constants for the systole map from the Teichmuller space to the curve complex. We give similar results to those known for closed surfaces in the cases when the genus is fixed or the ratio of genus and punctures is a rational number. Comment: 7 pages, 2 figures