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arXiv · 1111.5323

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

Boris Kolev·Vincent Guedj·Nader Yeganefar
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Abstract

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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Boris Kolev, Vincent Guedj, Nader Yeganefar. 2011-11-22. A Lichnerowicz estimate for the first eigenvalue of convex domains in Kähler manifolds. https://doi.org/10.2140/apde.2013.6.1001

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