2 problems

Let $M$ be a closed smooth manifold, and let $g$ be an $L^\infty$-metric on $M$, meaning that for some smooth reference Riemannian metric $g_0$ and constant $\Lambda>0$,…

Let $f\colon X\to Y$ be a projective surjective morphism between complex manifolds. Let $(L,h)$ be a holomorphic line bundle over $X$ equipped with a singular Hermitian metric of s…