Lengths and volumes in Riemannian manifolds

DOI10.1215/S0012-7094-04-12511-4zbMath1073.53053OpenAlexW1507144512WikidataQ115240302 ScholiaQ115240302MaRDI QIDQ1763075

Christopher B. Croke, Nurlan S. Dairbekov

Publication date: 21 February 2005

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-04-12511-4

zbMATH Keywords

volumelength spectrum

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Integral geometry (53C65) Rigidity results (53C24) Differential geometry of symmetric spaces (53C35) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20)

Related Items (11)

Comparison of volumes of Riemannian manifolds ⋮ Volume entropy and integral Ricci curvatures over closed geodesics ⋮ Approximate rigidity of the marked length spectrum ⋮ Marked boundary rigidity for surfaces of Anosov type ⋮ On filling minimality of simple Finsler manifolds ⋮ Simple root flows for Hitchin representations ⋮ A synthetic characterization of the hemisphere ⋮ Boundary rigidity with partial data ⋮ Marked length spectra and areas of non-positively curved cone metrics ⋮ The marked length spectrum of Anosov manifolds ⋮ Marked length rigidity for Fuchsian buildings

Cites Work

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• Rigidity and the distance between boundary points
• Le spectre marqué des longueurs des surfaces à courbure négative. (The spectrum marked by lengths of surfaces with negative curvature)
• Rigidity for surfaces of non-positive curvature
• Filling Riemannian manifolds
• The geometry of Teichmüller space via geodesic currents
• The marked length-spectrum of a surface of nonpositive curvature
• Geodesic rays, Busemann functions and monotone twist maps
• On the length of the geodesics of a metric of negative curvature on the disc.
• Entropy and rigidity of locally symmetric spaces of strictly negative curvature
• Local boundary rigidity of a compact Riemannian manifold with curvature bounded above
• Minimal entropy and Mostow's rigidity theorems
• On the Space of Invariant Measures for Hyperbolic Flows
• Sub-actions for Anosov flows

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