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math.DG2013
Proof of the Log-Convex Density Conjecture
Gregory R. Chambers
We completely characterize isoperimetric regions in R^n with density e^h, where h is convex, smooth, and radially symmetric. In particular, balls around the origin constitute isope…
math.DG2013
Monotone homotopies and contracting discs on Riemannian surfaces
Gregory R. Chambers, Regina Rotman
We prove a "gluing" theorem for monotone homotopies; a monotone homotopy is a homotopy through simple contractible closed curves which themselves are pairwise disjoint. We show tha…
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…