Stable bundles and the first eigenvalue of the Laplacian

LOI, ANDREA;AREZZO C;GHIGI A.

2007-01-01

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Abstract

In this article we study the first eigenvalue of the Laplacian on a compact manifold using stable bundles and balanced bases. Our main result is the following: Let M be a compact Kahler manifold of complex dimension n and E a holomorphic vector bundle of rank r over M. If E is globally generated and its Gieseker point T-E is stable, then for any Kahler metric g on M