The real Schwarz Lemma and geometric applications

DOI10.1007/BF02392826zbMath1035.53038OpenAlexW100527680MaRDI QIDQ1588922

Gérard Besson, Sylvestre Gallot, Gilles Courtois

Publication date: 6 December 2000

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02392826

zbMATH Keywords

symmetric spacesrigiditynegative curvatureminimal volumeminimal entropytotally geodesic submanifoldsquasi-Fuchsian representation

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Rigidity results (53C24) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45)

Related Items (19)

Maximal volume entropy rigidity for RCD∗(−(N−1),N) spaces ⋮ Diastatic entropy and rigidity of complex hyperbolic manifolds ⋮ Unnamed Item ⋮ Small eigenvalues of random 3-manifolds ⋮ Small volume of balls, large volume entropy and the Margulis constant ⋮ On Poincaré extensions of rational maps ⋮ Simplicial volume, barycenter method, and bounded cohomology ⋮ On the diastatic entropy and \(\mathcal{C}^1\)-rigidity of complex hyperbolic manifolds ⋮ Volume change under drilling ⋮ Volume comparison in the presence of a Gromov-Hausdorff \(\varepsilon\)-approximation. I ⋮ Volume invariant and maximal representations of discrete subgroups of Lie groups ⋮ Maximal volume representations are Fuchsian ⋮ Lower bounds on volumes of hyperbolic Haken 3-manifolds ⋮ Entropy rigidity of negatively curved manifolds of finite volume ⋮ Rigidity and \(L^2\) cohomology of hyperbolic manifolds ⋮ Constructing equivariant maps for representations ⋮ A vanishing theorem for the homology of discrete subgroups of Sp( n , 1) and F ₄ ^–20 ⋮ The rigidity on the second fundamental form of projective manifolds ⋮ Hyperbolic manifolds, amalgamated products and critical exponents

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