We give some theorems on algebraic dependence of meromorphic mappings in several complex variables into complex projective spaces.

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In this paper, we give some vanishing theorems for harmonic [Formula: see text]-forms on complete noncompact Riemannian manifolds satisfying a weighted [Formula: see text]-Poincaré inequality under the pointwise curvature pinching conditions which are bounded from above by the weight function. In some of our results, the condition on scalar curvature is no longer required as in previous ones.

UDC 517.53 We prove the unicity theorems for meromorphic mappings of a complete Kähler manifold into projective varieties† sharing few hypersurfaces in subgeneral position without counting multiplicities, where all zeros with multiplicities greater than a certain number are omitted.  We also present the uniqueness theorem in which the assumption of nondegeneracy of the mappings is no longer required.  These results are extensions and generalizations of some recent results.