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math.DG2009★ 1 cited
Closed geodesics in Alexandrov spaces of curvature bounded from above
Longzhi Lin
In this paper, we show a local energy convexity of maps into spaces. This energy convexity allows us to extend Colding and Minicozzi's width-sweepout constructio…
math.DG2009
Existence of Good Sweepouts on Closed Manifolds
Longzhi Lin, Lu Wang
In this note we establish estimates for the harmonic map heat flow from into a closed manifold, and use it to construct sweepouts with the following good property: each curve…