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A
Lichnerowicz estimate for the first eigenvalue of convex
domains in Kähler manifolds
Vincent Guedj, Boris Kolev and Nader Yeganefar |
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Vol. 6 (2013), No. 5, 1001–1012
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Abstract |
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In this article, we prove a Lichnerowicz estimate for a compact convex domain of a Kähler manifold whose Ricci curvature satisfies Ric for some constant . 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. |
Keywords
Lichnerowicz estimate, first eigenvalue, convex domains in
Kähler manifolds
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Mathematical Subject Classification 2010
Primary: 35P15, 58C40
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Milestones
Received: 25 January 2012
Revised: 10 June 2012
Accepted: 27 September 2012
Published: 3 November 2013
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Authors |
| Vincent Guedj | |
| Institut Universitaire de France and
Institut Mathematiques de Toulouse Universite Paul Sabatier 118 route de Narbonne F-31062 Toulouse Cedex 9 France |
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| Boris Kolev | |
| Laboratoire d’Analyse, Topologie,
Probabilités CNRS & Aix-Marseille University CMI 39 rue F. Joliot-Curie 13453 Marseille Cedex 13 France |
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| Nader Yeganefar | |
| Laboratoire d’Analyse, Topologie,
Probabilités Aix-Marseille University CMI 39 rue F. Joliot-Curie 13453 Marseille Cedex 13 France |
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