| 摘 要： | We discuss a class of complete Khler manifolds which are asymptotically complex hyperbolic near infinity . The main result is vanishing theorems for the second L2 cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincaré inequality case and establish a vanishing theorem provided that the weighted function ρ is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighte...
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