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2013 A Lichnerowicz estimate for the first eigenvalue of convex domains in Kähler manifolds
Vincent Guedj, Boris Kolev, Nader Yeganefar
Anal. PDE 6(5): 1001-1012 (2013). DOI: 10.2140/apde.2013.6.1001

Abstract

In this article, we prove a Lichnerowicz estimate for a compact convex domain of a Kähler manifold whose Ricci curvature satisfies Rick 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.

Citation

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Vincent Guedj. Boris Kolev. Nader Yeganefar. "A Lichnerowicz estimate for the first eigenvalue of convex domains in Kähler manifolds." Anal. PDE 6 (5) 1001 - 1012, 2013. https://doi.org/10.2140/apde.2013.6.1001

Information

Received: 25 January 2012; Revised: 10 June 2012; Accepted: 27 September 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1282.35262
MathSciNet: MR3125547
Digital Object Identifier: 10.2140/apde.2013.6.1001

Subjects:
Primary: 35P15, 58C40

Rights: Copyright © 2013 Mathematical Sciences Publishers

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