Total curvature and length estimate for curves in CAT(\(K\)) spaces.

DOI10.1016/S0926-2245(03)00031-7zbMath1039.51007WikidataQ115338024 ScholiaQ115338024MaRDI QIDQ1410601

Yongwimon Lenbury, Chaiwat Maneesawarng

Publication date: 14 October 2003

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

zbMATH Keywords

bounded curvaturelength estimatestotal curvature of curves

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 (6)

Total curvature and simple pursuit on domains of curvature bounded above ⋮ The Plateau-Douglas problem for singular configurations and in general metric spaces ⋮ Continuous pursuit curves on \(\mathrm{CAT}(K)\) spaces ⋮ Total curvature and some characterizations of closed curves in \(\mathrm{CAT}(k)\) spaces ⋮ The total intrinsic curvature of curves in Riemannian surfaces ⋮ Rubber bands, pursuit games and shy couplings

Cites Work

• Geometry IV. Non-regular Riemannian geometry. Transl. from the Russian by E. Primrose
• Upper estimates of the length of a curve in a Riemannian manifold with boundary
• Eine geometrische Bemerkung zu Sätzen über harmonische Abbildungen, die ein Dirichletproblem lösen
• Comparison theorems for curves of bounded geodesic curvature in metric spaces of curvature bounded above
• Inextensible mappings in a space of curvature no greater than K
• The Hadamard-Cartan theorem in locally convex metric spaces
• The Fary-Milnor theorem in Hadamard manifolds
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