K-correspondences and intrinsic pseudovolume forms

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We introduce the notion of K-correspondence, and show that many Calabi-Yau varieties carry a lot of self-K-isocorrespondences, which furthermore satisfy the property of multiplying the canonical volume form by a constant of modulus different from 1. This leads to the introduction of a modified Kobayashi-Eisenman pseudovolume form, for which we are able to prove many instances of the Kobayashi conjecture.