Monotone homotopies and contracting discs on Riemannian surfaces

DOI10.1142/S1793525318500103zbMath1395.53035arXiv1311.2995OpenAlexW2963055090WikidataQ115244567 ScholiaQ115244567MaRDI QIDQ4565336

Gregory R. Chambers, Regina Rotman

Publication date: 12 June 2018

Published in: Journal of Topology and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.2995

zbMATH Keywords

metric geometryquantitative topologyhomotopies of curves on surfaces.

Mathematics Subject Classification ID

Spaces of embeddings and immersions (58D10) Global Riemannian geometry, including pinching (53C20) Homotopy groups (55Q99)

Related Items (3)

Existence of minimal hypersurfaces in complete manifolds of finite volume ⋮ Constructing monotone homotopies and sweepouts ⋮ Computing Optimal Homotopies over a Spiked Plane with Polygonal Boundary

Cites Work

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• Length of geodesics and quantitative Morse theory on loop spaces
• Linear bounds for lengths of geodesic loops on Riemannian 2-spheres
• Converting homotopies to isotopies and dividing homotopies in half in an effective way
• The Morse landscape of a Riemannian disk
• Contracting the boundary of a Riemannian 2-disc
• Area and the length of the shortest closed geodesic
• LINEAR BOUNDS FOR LENGTHS OF GEODESIC SEGMENTS ON RIEMANNIAN 2-SPHERES
• Surfaces of small diameter with large width
• Diastolic and isoperimetric inequalities on surfaces
• Spheres of small diameter with long sweep-outs
• Contracting thin disks
• Splitting a contraction of a simple curve traversed m times

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