Tangent cut loci on surfaces

DOI10.1016/j.difgeo.2011.02.002zbMath1217.53038OpenAlexW2057538475WikidataQ112632030 ScholiaQ112632030MaRDI QIDQ531730

Alessio Figalli, Ludovic Rifford, Cédric Villani

Publication date: 19 April 2011

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2011.02.002

zbMATH Keywords

Riemannian manifoldscut locussemiconcave functionsinjectivity domains

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global Riemannian geometry, including pinching (53C20)

Related Items (6)

The Azimuthal equidistant projection for a Finsler manifold by the exponential map ⋮ Computing the cut locus of a Riemannian manifoldviaoptimal transport ⋮ Singularities of dual hypersurfaces and hyperbolic focal surfaces along spacelike curves in light cone in Minkowski 5-space ⋮ Singularities of indefinite hypersurfaces and indefinite surfaces along timelike curves in nullcone with index two ⋮ Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds ⋮ On the Convexity of Injectivity Domains on Nonfocal Manifolds

Cites Work

• Unnamed Item
• On the Ma-Trudinger-Wang curvature on surfaces
• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Regularity of optimal transport in curved geometry: the nonfocal case
• Metric structure of cut loci in surfaces and Ambrose's problem
• The cut loci and the conjugate loci on ellipsoids
• Regularity of potential functions of the optimal transportation problem
• Nearly Round Spheres Look Convex
• The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations
• Regularity properties of the distance functions to conjugate and cut loci for viscosity solutions of Hamilton-Jacobi equations and applications in Riemannian geometry
• Continuity of optimal transport maps and convexity of injectivity domains on small deformations of 𝕊²
• The Lipschitz continuity of the distance function to the cut locus
• Optimal Transport
• Riemannian geometry

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