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In this paper, we establish a truncated non-integrated defect relation formeromorphic mappings from a complete K\"ahler manifold into a projectivevariety intersecting a family of hypersurfaces located in subgeneral position,where the truncation level of the defect is explicitly estimated. Our resultgeneralizes and improves previous ones. In particular, when the family ofhypersurfaces located in general position, our theorem will implies theprevious result of Min Ru-Sogome. In the last part of this paper we will applyours to study the distribution of the Gauss map of minimal surfaces.

Non-integrated defect relation for meromorphic mappings from a K\"ahler manifold with hypersurfaces of a projective variety in subgeneral position