13 problems

Let $\Omega\subset\mathbb{C}^n$ be a pseudoconvex domain, and let $A^2(\Omega)$ denote its Bergman space of square-integrable holomorphic functions. Property (2.1) is the property…

Let $M\subset \mathbb{C}^n$ be a pseudoconvex real hypersurface with $n\geq 3$. For $1\leq s\leq n-2$ and $p\in M$, write $t^{(s)}(M,p)$, $c^{(s)}(M,p)$ and $a^{(s)}(M,p)$ for the…

Let $M$ be a compact Kähler manifold of dimension $k$, and let $E$ be a holomorphic $\mathbb{B}^n$-bundle over $M$ embedded in the associated $\mathbb{CP}^n$-bundle $\widehat{E}$.…

Let $X$ be a weakly pseudoconvex Kähler complex space. Its regular locus is denoted by $X_{\operatorname{reg}}$, and an analytic subset of a complex space is denoted by $A$. Comple…

Let $M$ be a pseudoconvex hypersurface in $\mathbb{C}^n$, and let $q$-dimensional complex manifolds and $q$-dimensional subbundles of the $(1,0)$ tangent space of $M$ be considered…

Let $q_0\in\mathcal{Q}_g$ be generic, meaning that $q_0$ lies in the principal stratum. Let $T^H_{q_0}\mathcal{Q}_g$ denote a horizontal lift determined by a guiding frame, and let…

D'Angelo's conjecture. One has

Let $M\subset \mathbb{C}^n$ be a pseudoconvex real hypersurface with $n\geq 3$, let $1\leq s\leq n-2$, let $p\in M$, and let $B$ be a smooth complex vector subbundle of…

Let $M\subset \mathbb{C}^n$ be a pseudoconvex real hypersurface, let $p\in M$, and let $L$ be a complex vector field in the relevant $(1,0)$ tangent directions. Denote by…

Let $\Omega$ be a family of domains, and consider the associated direct image bundles and their curvature. The family is strictly pseudoconvex when its defining function has the re…

Let $\mathcal D$ be a pseudoconvex domain with smooth boundary in a complex manifold $\mathcal{M}$ of dimension at least $3$. Let $\mathfrak{B}$ be the set of all weakly pseudoconv…

Let $\Omega$ be an open bounded domain in $\mathbb{C}^{n}$ with smooth and strictly pseudoconvex boundary, let $\beta\in[0,\infty[$, and let…

Let $\Omega$ be a strictly pseudoconvex domain, and consider the equivalence of the following four conditions for the graph $\mathcal G_h(b\Omega)$ and functions $h_1,\ldots,h_N$:…