5 problems

Let $\Omega \subset \mathbb{C}^n$, $n \geq 1$, be a bounded domain. Write $R^\Omega$ for the curvature tensor of its Bergman metric, and let…

Let $\Omega$ be a bounded symmetric domain of rank $r$, with invariants $p$, $b$, $d$, and $q_\Omega$, and let $\Gamma_\Omega$ denote the associated gamma function. Let $m$ and…

Let $D^{\mathrm{I}}_{p,q}$ denote the irreducible type-I bounded symmetric domain, and let $F:D^{\mathrm{I}}_{p,q}\to D^{\mathrm{I}}_{p',q'}$ be a proper holomorphic map, where…

Type-IV total geodesy conjecture. Then

Rank-2 type-I total geodesy conjecture. If