Comparison theorems for curves of bounded geodesic curvature in metric spaces of curvature bounded above

DOI10.1016/0926-2245(96)00008-3zbMath0859.53053OpenAlexW2062054048WikidataQ115362514 ScholiaQ115362514MaRDI QIDQ1917367

Richard L. Bishop, Stephanie B. Alexander

Publication date: 7 July 1996

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

Full work available at URL: https://doi.org/10.1016/0926-2245(96)00008-3

zbMATH Keywords

curvature bounded abovegeodesic curvatureCAT(K) spaceconvexity of balls

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global Riemannian geometry, including pinching (53C20) Direct methods ((G)-spaces of Busemann, etc.) (53C70) Synthetic differential geometry (51K10)

Related Items (17)

Warped products admitting a curvature bound ⋮ The Dirichlet problem for harmonic maps from Riemannian polyhedra to spaces of upper bounded curvature ⋮ Collapsing manifolds with boundary ⋮ Weyl's law for singular Riemannian manifolds ⋮ Total curvature and length estimate for curves in CAT(\(K\)) spaces. ⋮ Metric Curvatures Revisited: A Brief Overview ⋮ Continuous pursuit curves on \(\mathrm{CAT}(K)\) spaces ⋮ Complex surfaces with CAT(0) metrics ⋮ Total curvature and some characterizations of closed curves in \(\mathrm{CAT}(k)\) spaces ⋮ Harmonic maps from Riemannian polyhedra to geodesic spaces with curvature bounded from above ⋮ The Jung Theorem in metric spaces of curvature bounded above ⋮ Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above ⋮ Completions, branched covers, Artin groups, and singularity theory ⋮ Extrinsic curvature of semiconvex subspaces in Alexandrov geometry ⋮ Metric Ricci Curvature and Flow for PL Manifolds ⋮ Conjugate points in length spaces ⋮ Three-manifolds of positive curvature and convex weakly umbilic boundary

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