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Article Dans Une Revue Analysis & PDE Année : 2013

A Lichnerowicz estimate for the first eigenvalue of convex domains in Kähler manifolds

Résumé

In this article, we prove a Lichnerowicz estimate for a compact convex domain of a Kähler manifold whose Ricci curvature satisfies $\Ric \ge k$ for some constant $k>0$. When equality is achieved, the boundary of the domain is totally geodesic and there exists a nontrivial holomorphic vector field. We show that a ball of sufficiently large radius in complex projective space provides an example of a strongly pseudoconvex domain which is not convex, and for which the Lichnerowicz estimate fails.
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Dates et versions

hal-00643603 , version 1 (22-11-2011)

Identifiants

Citer

Vincent Guedj, Boris Kolev, Nader Yeganefar. A Lichnerowicz estimate for the first eigenvalue of convex domains in Kähler manifolds. Analysis & PDE, 2013, 6 (5), pp.1001-1012. ⟨10.2140/apde.2013.6.1001⟩. ⟨hal-00643603⟩
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