2 problems

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The degree positivity conjecture for Lee classes on LCK manifolds
Degree positivity conjecture. If $\theta$ is a Lee class, then
Conjectureopencomplex-geometry gauduchon-metrics lck-manifoldsarXiv posted 2 days ago
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The Bott–Chern positivity conjecture for Lee forms
Bott–Chern positivity conjecture. The $(1,1)$ -form $-d(I\theta)$ is Bott–Chern homologous to a positive $(1,1)$ -current.
Conjectureopenbott-chern-cohomology complex-geometry lck-manifoldsarXiv posted 2 days ago

The degree positivity conjecture for Lee classes on LCK manifolds