On 𝐿² cohomology of ACH Kähler manifolds

Wang, Xiaodong

doi:10.1090/S0002-9939-07-08838-7

On $L^2$ cohomology of ACH Kähler manifolds
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Proc. Amer. Math. Soc. 135 (2007), 2949-2960 Request permission

Abstract:

We discuss a class of complete Kähler manifolds which are asymptotically complex hyperbolic near infinity. The main result is a sharp vanishing theorem for the second $L^2$ cohomology of such manifolds under certain assumptions. The borderline case characterizes a Kähler-Einstein manifold constructed by Calabi.

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