Bottom of spectrum of Kahler manifolds with strongly pseudoconvex boundary

Mathematics – Differential Geometry

Scientific paper

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Scientific paper

We consider a class of complete Kahler manifolds with a strictly pseudoconvex
boundary at infinity. After studying its asymptotic geometry, we formulate a
conjecture in the Kahler-Einstein case relating the bottom of spectrum to the
CR geometry on the boundary. We prove some partial results.

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