Related papers: Local Plurisubharmonic Defining Functions on the B…
In the spirit of Lelong and Bochner, we show that an upper semi-continuous function defined on a open tube set $\Omega=\omega + i\mathbb{R}^n$ in $\mathbb{C}^n$, where $\omega$ is an open set in $\mathbb{R}^n$, and which is invariant in its…
We discuss the existence of positive superharmonic functions $u$ in $\mathbb{R}^N_+=\mathbb{R}^{N-1}\times (0, \infty)$, $N\geq 3$, in the sense $-\Delta u=\mu$ for some Radon measure $\mu$, so that $u$ satisfies the nonlocal boundary…
Let $\Omega$ be a strongly pseudoconvex domain. We introduce the Mabuchi space of strongly plurisubharmonic functions in $\Omega$. We study metric properties of this space using Mabuchi geodesics and establish regularity properties of the…
We analyze the topological structure of the Nehari set for a class of functionals depending on a real parameter $\lambda$, and having two degrees of homogeneity. A special attention is paid to the extremal parameter $\lambda^*$, which is…
The (unbounded version of the) Lempert function $l_D$ on a domain $D\subset\Bbb C^d$ does not usually satisfy the triangle inequality, but on bounded $\mathcal C^2$-smooth strictly pseudoconvex domains, it satisfies a quasi triangle…
In this paper, we obtain \textit{quantitative} estimates on the fine structure of the singular set of the mutual boundary $\partial \Omega^{\pm}$ for pairs of complementary domains, $\Omega^+, \Omega^- \subset \mathbb{R}^n$ which arise in a…
We ask under what conditions on the function $f$, and a set of maps $\mathcal T$, it is the case that $f$ is a coboundary for some map in $\mathcal T$. We also consider for a function $f$, and a set of maps $\mathcal T$, when we have $f$…
Let $\varphi $ be a negative plurisubharmonic function in a pseudoconvex domain $\Omega$ in $\mathbb{C}^{n}$ and $f$ be a bounded holomorphic function belonging to $L^{2}(\Omega, \varphi)$. For all negative plurisubharmonic functions $\psi$…
The classical results about the boundary values of holomorphic or harmonic functions on a domain $D$ state that under additional integrability assumptions these functions have limits along specific sets approaching boundary. The proofs of…
For a bounded domain equipped with a piecewise Lipschitz continuous Riemannian metric g, we consider harmonic map from $(\Omega, g)$ to a compact Riemannian manifold $(N,h)\subset\mathbb R^k$ without boundary. We generalize the notion of…
We give a necessary condition for a meromorphic function in several variables to give rise to a Milnor fibration of the local link (respectively of the link at infinity). In the case of two variables we give some necessary and sufficient…
The aim of this paper is first to give necessary and sufficient condition of existence (of free boundaries) for both Laplacian and bi-Laplacian operators in the case where the overdetermined condition is not constant. second, by using some…
Let $(M,\omega)$ be a Kahler manifold. An integrable function on M is called $\omega^q$-plurisubharmonic if it is subharmonic on all q-dimensional complex subvarieties. We prove that a smooth $\omega^q$-plurisubharmonic function is…
We study a composition operator on Lorentz spaces. In particular we provide necessary and sufficient conditions under which a measurable mapping induces a bounded composition operator.
We introduce Robin boundary conditions for biharmonic operators, which are a model for elastically supported plates and are closely related to the study of spaces of traces of Sobolev functions. We study the dependence of the operator, its…
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…
The paper is devoted to a detailed analysis of nonlocal error bounds for nonconvex piecewise affine functions. We both improve some existing results on error bounds for such functions and present completely new necessary and/or sufficient…
It is established that if a harmonic function $u$ on the unit disk $\mathbb D$ in $\mathbb C$ has angular limits on a measurable set $E$ of the unit circle $\partial\mathbb D$, then its conjugate harmonic function $v$ in $\mathbb D$ also…
In this paper, by reviewing the concept of subcovering and semicovering maps, we extend the notion of subcovering map to subsemicovering map. We present some necessary or sufficient conditions for a local homeomorphism to be a…
In the present paper we establish the Wiener test for boundary regularity of the solutions to the polyharmonic operator. We introduce a new notion of polyharmonic capacity and demonstrate necessary and sufficient conditions on the capacity…