3 problems

Let $S^{2}$ be the two-sphere, let $\mu$ be the measure used in the definitions of the functionals $A_{n}$ and $B_{n}$, and let $A_{n}(\varphi)$ and $B_{n}(\varphi)$ be the corresp…

Let $C$ be a smooth closed curve with canonical constant-curvature metric $g_{0}^{C}$, and let $l$ be a holomorphic line bundle with induced canonical metric $g_{0}^{l}$. For a Her…

Let $C$ be a compact complex curve with Hermitian metric $g^{C}$, and let $l$ be a line bundle over $C$ with associated Hermitian metric $g^{l}$. Write $A(g^{C},g^{l})$ for the log…