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Article Dans Une Revue Communications in Mathematical Physics Année : 2020

The Cheeger constant of an asymptotically locally hyperbolic manifold and the Yamabe type of its conformal infinity

Résumé

Let (M, g) be an (n + 1)-dimensional asymptotically locally hyperbolic (ALH) manifold with a conformal compactification whose conformal infinity is (∂M, [γ]). We will first observe that Ch(M, g) ≤ n, where Ch(M, g) is the Cheeger constant of M. We then prove that, if the Ricci curvature of M is bounded from below by −n and its scalar curvature approaches −n(n+1) fast enough at infinity, then Ch(M, g) = n if and only Y(∂M, [γ]) ≥ 0, where Y(∂M, [γ]) denotes the Yamabe invariant of the conformal infinity. This gives an answer to a question raised by J. Lee [L].
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Dates et versions

hal-02282559 , version 1 (10-09-2019)

Identifiants

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Oussama Hijazi, Sebastian Montiel, Simon Raulot. The Cheeger constant of an asymptotically locally hyperbolic manifold and the Yamabe type of its conformal infinity. Communications in Mathematical Physics, 2020, 374, pp.873-890. ⟨10.1007/s00220-019-03545-x⟩. ⟨hal-02282559⟩
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