2 problems

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The converse from Kollár-hyperbolicity to V-hyperbolicity
Converse conjecture. If $X$ is Kollár-hyperbolic with respect to $H$ , then $X$ is V-hyperbolic with respect to $H$ .
Conjectureopencohomology etale-fundamental-groups hyperbolic-varietiesarXiv posted 2 days ago
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A vanishing conjecture for Kollár-hyperbolic varieties
Vanishing conjecture for Kollár-hyperbolic varieties. Kollár-hyperbolic varieties satisfy a vanishing theorem: in every nonzero degree, the limit of the normalized dimensions of th…
Conjectureopenetale-covers hyperbolic-varieties mixed-hodge-modulesarXiv posted 2 days ago

The converse from Kollár-hyperbolicity to V-hyperbolicity