TY - JOUR
T1 - Comparison theorem for kähler manifolds and positivity of spectrum
AU - Li, Peter
AU - Wang, Jiaping
PY - 2005
Y1 - 2005
N2 - The first part of this paper is devoted to proving a comparison theorem for Kähler manifolds with holomorphic bisectional curvature bounded from below. The model spaces being compared to are ℂℙm, ℂm, and ℂℍm. In particular, it follows that the bottom of the spectrum for the Laplacian is bounded from above by m2 for a complete, m-dimensional, K�ahler manifold with holomorphic bisectional curvature bounded from below by −1. The second part of the paper is to show that if this upper bound is achieved and when m = 2, then it must have at most four ends.
AB - The first part of this paper is devoted to proving a comparison theorem for Kähler manifolds with holomorphic bisectional curvature bounded from below. The model spaces being compared to are ℂℙm, ℂm, and ℂℍm. In particular, it follows that the bottom of the spectrum for the Laplacian is bounded from above by m2 for a complete, m-dimensional, K�ahler manifold with holomorphic bisectional curvature bounded from below by −1. The second part of the paper is to show that if this upper bound is achieved and when m = 2, then it must have at most four ends.
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U2 - 10.4310/jdg/1121540339
DO - 10.4310/jdg/1121540339
M3 - Article
AN - SCOPUS:33744975029
SN - 0022-040X
VL - 69
SP - 43
EP - 74
JO - Journal of Differential Geometry
JF - Journal of Differential Geometry
IS - 1
ER -