Entropies et rigidités des espaces localement symétriques de courbure strictement négative

Besson, Gérard; Courtois, G.; Gallot, Sylvestre

doi:10.1007/bf01897050

Cited by 346 publications

(570 citation statements)

References 36 publications

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“…Let us now consider a natural family of minimal volume invariants [15,7,28] defined with respect to only lower bounds on curvature. Let M be any smooth compact manifold of dimension n. By just considering large constant multiples of some given metric, one obtains metrics on on M with sectional curvature K ≥ −1, at the price of making the total volume of M enormous.…”

Section: Sectional Curvature and Volumementioning

confidence: 99%

Ricci curvature, minimal volumes, and Seiberg-Witten theory

LeBrun

2001

Inventiones Mathematicae

104

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We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4-manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum of the L 2 -norm of Ricci curvature for all complex surfaces of general type. We are also able to show that the standard metric on any complex hyperbolic 4-manifold minimizes volume among all metrics satisfying a point-wise lower bound on sectional curvature plus suitable multiples of the scalar curvature. These estimates also imply new non-existence results for Einstein metrics.

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Section: Sectional Curvature and Volumementioning

confidence: 99%

Ricci curvature, minimal volumes, and Seiberg-Witten theory

LeBrun

2001

Inventiones Mathematicae

104

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“…For simple Lie groups it is shown in ( [6]). Along this line, Besson, Courtois, Gallot and Hamenstädt ( [2], [9]) showed that, if M is a negatively curved locally symmetric compact manifold and N is an arbitrary negatively curved manifold which has the same marked length spectrum with M , then they are isometric. Actually it is conjectured that two negatively curved compact manifolds with the same marked length spectrum are isometric.…”

Section: Introductionmentioning

confidence: 99%

Marked length rigidity for symmetric spaces

Kim

2002

Commentarii Mathematici Helvetici

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“…As in the case of all noncompact situations, to apply the method of [BCG1] and [BCG5], the fundamental difficulty is proving the properness of the natural map.…”

Section: And Equality Holds If and Only If M And M O Are Hyperbolic Amentioning

confidence: 99%