The Lipschitz continuity of the distance function to the cut locus

From MaRDI portal
Publication:4510021

DOI10.1090/S0002-9947-00-02564-2zbMath0971.53031OpenAlexW1531971668MaRDI QIDQ4510021

Jin-ichi Itoh, Minoru Tanaka

Publication date: 19 October 2000

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-00-02564-2




Related Items (49)

The Azimuthal equidistant projection for a Finsler manifold by the exponential mapDensity problems for W1,1 (M, N)Computing the cut locus of a Riemannian manifoldviaoptimal transportApproximations of Lipschitz maps via Ehresmann fibrations and Reeb's sphere theorem for Lipschitz functionsLoki: Software for Computing Cut LociOn differentiability of volume time functionsThe central set and its application to the Kneser-Poulsen conjectureA characterization of cut locus for \(C^1\) hypersurfacesThe Monge–Ampère equation and its link to optimal transportationLinking curves, sutured manifolds and the Ambrose conjecture for generic 3-manifoldsOn the Ma-Trudinger-Wang curvature on surfacesThe distance function from the boundary of a domain with cornersRegularity of the distance function from arbitrary closed setsSome sharp isoperimetric-type inequalities on Riemannian manifoldsBalanced split sets and Hamilton-Jacobi equationsCut and singular loci up to codimension 3A geometric characterization of a sharp Hardy inequalityA new family of latitudinally corrugated two-spheres of revolution with simple cut locus structureAlexandrov's isodiametric conjecture and the cut locus of a surfaceThe Dirichlet random walkThe sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometryA nonhomogeneous boundary value problem in mass transfer theoryGeneralized von Mangoldt surfaces of revolution and asymmetric two-spheres of revolution with simple cut locus structureA new symmetry criterion based on the distance function and applications to PDE'sTotal curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. IToponogov comparison theorem for open trianglesOn the characterization of some classes of proximally smooth setsThe cut locus of a two-sphere of revolution and Toponogov's comparison theoremDistance functions with dense singular setsRegularity of optimal transport in curved geometry: the nonfocal caseTangent cut loci on surfacesRegularity properties of the distance functions to conjugate and cut loci for viscosity solutions of Hamilton-Jacobi equations and applications in Riemannian geometryOrbifold compactness for spaces of Riemannian metrics and applicationsThe distance function from the boundary in a Minkowski spaceRegularity and variationality of solutions to Hamilton-Jacobi equations. Part I: Regularity (errata)Uncertainty principles on compact Riemannian manifoldsApplications of cone structures to the anisotropic rheonomic Huygens' principleTotal curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. IIRegularity and variationality of solutions to Hamilton-Jacobi equations. Part I: RegularityThe distance from the boundary in a Riemannian manifold: regularity up to a conformal change of the metricOn some aspects of oscillation theory and geometryContinuity of optimal transport maps and convexity of injectivity domains on small deformations of 𝕊2Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifoldsHölder regularity of the normal distance with an application to a PDE model for growing sandpilesHomotopic distance and generalized motion planningThe structure theorem for the cut locus of a certain class of cylinders of revolution. I.A boundary value problem for a PDE model in mass transfer theory: representation of solutions and applicationsOn the Convexity of Injectivity Domains on Nonfocal ManifoldsOn fine differentiability properties of horizons and applications to Riemannian geometry



Cites Work


This page was built for publication: The Lipschitz continuity of the distance function to the cut locus