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math.DG2013
Converting homotopies to isotopies and dividing homotopies in half in an effective way
Gregory R. Chambers, Yevgeny Liokumovich
We prove two theorems about homotopies of curves on 2-dimensional Riemannian manifolds. We show that, for any epsilon > 0, if two simple closed curves are homotopic through curves…
math.DG2013
Surfaces of small diameter with large width
Yevgeny Liokumovich
Given a 2-dimensional surface M and a constant C we construct a Riemannian metric g, so that diameter diam(M,g)=1 and every 1-cycle dividing M into two regions of equal area has le…