Related papers: Kobayashi-Royden vs. Hahn pseudometric in ${\Bbb C…

Let ${H^p}\left( \mathbb{D} \right)$ be the Hardy space of all holomorphic functions on the unit disk $\mathbb{D}$ with exponent $p>0$. If $D\ne \mathbb{C}$ is a simply connected domain and $f$ is the Riemann mapping from $\mathbb{D}$ onto…

The Fock-Bargmann-Hartogs domain $D_{n,m}(\mu)$ ($\mu>0$) in $\mathbb{C}^{n+m}$ is defined by the inequality $\|w\|^2<e^{-\mu\|z\|^2},$ where $(z,w)\in \mathbb{C}^n\times \mathbb{C}^m$, which is an unbounded non-hyperbolic domain in…

A flag domain $D$ is an open orbit of a real form $G_0$ in a flag manifold $Z=G/P$ of its complexification. If $D$ is holomorphically convex, then, since it is a product of a Hermitian symmetric space of bounded type and a compact flag…

For a domain $D \subset \mathbb C^n$, $n \ge 2$, let $F^k_D(z)=K_D(z)\lambda\big(I^k_D(z)\big)$, where $K_D(z)$ is the Bergman kernel of $D$ along the diagonal and $\lambda\big(I^k_D(z)\big)$ is the Lebesgue measure of the Kobayashi…

Of the two approaches to integrable systems associated to semisimple cohomological field theories (CohFTs), the one suggested by Dubrovin and Zhang and the more recent one using the geometry of the double ramification (DR) cycle, the second…

We compute the second Hochschild cohomology space $HH^2(\mathcal{H}_1)$ of Connes-Moscovici's Hopf algebra $\mathcal{H}_1$, giving the infinitesimal deformations (up to equivalence) of the associative structure. $HH^2(\mathcal{H}_1)$ is…

Let $(K,d)$ be a connected compact metric space and $p\in (1, \infty)$. Under the assumption of \cite[Assumption 2.15]{Ki2} and the conductive $p$-homogeneity, we show that $\mathcal{W}^p(K)\subset C(K)$ holds if and only if…

Bousfield and Kan's $\mathbb{Q}$-completion and fiberwise $\mathbb{Q}$-completion of spaces lead to two different approaches to the rational homotopy theory of non-simply connected spaces. In the first approach, a map is a weak equivalence…

Uniformly quasiconformally homogeneous domains in $\mathbb{R}^n$ carry a transitive collection of $K$-quasiconformal maps for a fixed $K\geq 1.$ In this paper, we study two questions in this setting. The first is to show that…

We show that the Voronoi conjecture is true for parallelohedra with simply connected $\delta$-surface. Namely, we show that if the boundary of parallelohedron $P$ remains simply connected after removing closed non-primitive faces of…

We introduce a covering notion depending on two cardinals, which we call $\mathcal O $-$ [ \mu, \lambda ]$-compactness, and which encompasses both pseudocompactness and many other generalizations of pseudocompactness. For Tychonoff spaces,…

In this article, we consider a bounded pseudoconvex domain in ${\bf C}^2$ satifying: (a) it admits a proper holomorphic mapping $f$ onto the unit ball $B^2$, and (b) it is simply connected and has a real analytic boundary. According to…

We prove a sharp bound for the minimal doubling of a small measurable subset of a compact connected Lie group. Namely, let $G$ be a compact connected Lie group of dimension $d_G$, we show that for for all measurable subsets $A$, we have…

It is an observation due to J.J. Kohn that for a smooth bounded pseudoconvex domain D in $C^n$ there exists s>0 such that the dbar-Neumann operator on D maps $W^s_{(0,1)}(D)$ (the space of $(0,1)$-forms with coefficient functions in…

The Kobayashi pseudometric on a complex manifold is the maximal pseudometric such that any holomorphic map from the Poincar\'e disk to the manifold is distance-decreasing. Kobayashi has conjectured that this pseudometric vanishes on…

We describe the strong dual space $({\mathcal O} (D))^*$ for the space ${\mathcal O} (D)$ of holomorphic functions of several complex variables over a bounded Lipschitz domain $D$ with connected boundary $\partial D$ (as usual, ${\mathcal…

We study the infimal value of the Hausdorff dimension of spaces that are H\"older equivalent to a given metric space; we call this bi-H\"older-invariant "H\"older dimension". This definition and some of our methods are analogous to those…

The main result is that for a connected hyperbolic complete K\"ahler manifold with bounded geometry of order two and exactly one end, either the first compactly supported cohomology with values in the structure sheaf vanishes or the…

In this paper we prove that given a pair $(X,D)$ of a threefold $X$ and a boundary divisor $D$ with mild singularities, if $(K_X+D)$ is movable, then the orbifold second Chern class $c_2$ of $(X,D)$ is pseudo-effective. This generalizes the…

D-dimensional maximal supergravities type I with G/H coset spaces have global G-symmetry and local H symmetry, which can be gauge-fixed in symmetric or Iwasawa-type gauges. Maximal D-dimensional supergravities type II derived from higher…