Contracting thin disks
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🧮 math.DG
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answerareaboundaryboundedcontractingcurvesdiameterdisc
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We answer a question of Liokumovich-Nabutovsky-Rotman showing that if D is a Riemannian 2-disc with boundary length L, diameter d and area A << d then D can be filled by a homotopy where the lengths of the intermediate curves are bounded by $L+2d+O(\sqrt A)$.
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