Bottom of Spectrum of Kahler Manifolds with Strongly Pseudoconvex Boundary
نویسندگان
چکیده
Theorem 1. Suppose (M; g) is a noncompact complete Riemannian manifold with Ric (n 1), we have 0 (n 1) =4. The estimate is sharp since the spectrum is the ray [(n 1) =4;+1) for the hyperbolic space H. For Kähler manifolds, this estimate can be improved. On a Kähler manifold (M; g) of complex dimension n, where g is the Riemannian metric, let ! = g (J ; ) be the Kähler form. In local holomorphic coordinates z1; ; zn, we have
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