Related papers: The Kobayashi pseudometric for the Fock-Bargmann-H…

In this paper, we construct a pseudoconvex domain in $\mathbb C^3$ where the Kobayashi metric does not blow up at a rate of one over distance to the boundary in the normal direction.

After a study of the Kobayashi metrics on certain scaled domains, we show the stabilities of the infinitesimal Kobayashi metrics and the integrated distances in different scaling processes. As an application, we prove that bounded…

We apply integral representations for functions on non-smooth strictly pseudoconvex domains, the Henkin-Leiterer domains, to derive weighted $C^k$ estimates for the component of a given function, $f$, which is orthogonal to holomorphic…

We characterize certain noncommutative domains in terms of noncommutative holomorphic equivalence via a pseudometric that we define in purely algebraic terms. We prove some properties of this pseudometric and provide an application to free…

In this paper we introduce a new class of domains in complex Euclidean space, called Goldilocks domains, and study their complex geometry. These domains are defined in terms of a lower bound on how fast the Kobayashi metric grows and an…

Let $\Omega_1$, $\Omega_2$ be two domains in $\mathbb{C}^n$ with Kobayashi metrics $k_{\Omega_i}$ and consider $f \in \mathcal{O}(\Omega_1,\Omega_2)$ a holomorphic mapping. Let $\mathfrak{F}_1$ and $\mathfrak{F}_2$ be a family of geodesics…

We prove that Kobayashi isometries between strongly convex domains are holomorphic or anti-holomorphic. More precisely, let $n_1, n_2$ be positive integers and let $\Omega_i \subset \C^{n_i}, \ i=1,2$, be bounded $C^3$ strongly convex…

We estimate the boundary behavior of the Kobayashi metric on $\C\sm\set{0,1}$. We also compare the Bergman metric on the ring domain in $\C^{2}$ to the Bergman metric on the ball.

We show some lower estimates for the Kobayashi-Royden metric on a class of smooth bounded pseudoconvex domains.

We prove the non-hyperbolicity of the Kobayashi distance for $\mathcal{C}^{1,1}$-smooth convex domains in $\mathbb{C}^{2}$ which contain an analytic disc in the boundary or have a point of infinite type with rotation symmetry. Moreover,…

In this paper we introduce new characterizations of spectral fractional Laplacian to incorporate nonhomogeneous Dirichlet and Neumann boundary conditions. The classical cases with homogeneous boundary conditions arise as a special case. We…

We show that every homeomorphic $W^{1,1}_{\rm loc}$ solution $f$ to a Beltrami equation $\bar{\partial}f=\mu \partial f$ in a domain $D\subset\Bbb C$ is the so--called lower $Q-$homeomorphism with $Q(z)=K^T_{\mu}(z, z_0)$ where…

This paper establishes quantitative Carleman-type inequalities for holomorphic sections of Hermitian vector bundles over bounded domains in $\mathbb{C}^n$ with $n \geq 2$. We first prove a Sobolev-type inequality with explicit constants for…

Let $\Omega$ be a bounded pseudoconvex Hartogs domain. There exists a natural complete K\"ahler metric $g^{\Omega}$ in terms of its defining function. In this paper, we study two problems. The first one is determining when $g^{\Omega}$ is…

This paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation $c(x)\partial_{t}^{2}u - \Delta u = 0$ in a bounded smooth domain in $\R^{d}$ from partial (on part of the boundary) dynamic…

We first give a sufficient condition, issued from pluripotential theory, for an unbounded domain in the complex Euclidean space $\mathbb C^n$ to be Kobayashi hyperbolic. Then, we construct an example of a rigid pseudoconvex domain in…

The relationship between the metric and nonrelativistic matter distribution depends on the theory of gravity and additional fields, providing a possible way of distinguishing competing theories. With the assumption that the geometry and…

In this paper, we study a model which is composed by the cosmological constant and dark matter with nonzero equation of state parameter, which could be called as $\Lambda$wDM. In the synchronous gauge, we obtain the perturbation equations…

Let D be a Hartogs domain of the form D={(z,w) \in CxC^N : |w| < e^{-u(z)}} where u is a subharmonic function on C. We prove that the Bergman space of holomorphic and square integrable functions on D is either trivial or infinite…

Bounded symmetric domains carry several natural invariant metrics, for example the Carath\'eodory, Kobayashi or the Bergman metric. We define another natural metric, from generalized Hilbert metric defined in [FGW20], by considering the…