On some second main theorems for meromorphic mappings of complete Kähler manifolds with hyperplanes and their applications

UDC 514.7 We establish the second main theorems for meromorphic mappings of complete Kähler manifolds into complex projective spaces with hyperplanes in the general position. This is a continuation of the works by Atsuji J. Math. Soc. Japan, 60, № 2, 471–493 (2008) and Dong J. Inst. Math. Jussieu, 1–29 (2022). We extend the results of these works to targets of higher dimension. As an application, we show that every meromorphic mapping of a complete Kähler manifold of nonpositive Ricci curvature and maximal volume growth into complex projective spaces with small growth, as compared to a half of the traceless Ricci curvature of the manifold, must be constant.