Related papers: On meromorphic functions defined by a differential…
Solutions describing holographic surface defects in $D=5,N=4$ gauged supergravity theories are constructed. It is shown that a surface defect solution in pure Romans' gauged supergravity is singular. Adding a single vector multiplet allows…
Let $D$ be a proper domain in the extended complex plane ${\mathbb C}_{\infty}:={\mathbb C}\cup \{\infty\}$, $M=M_+-M_-\not\equiv \pm \infty$ be a difference of non-trivial subharmonic functions $M_{\pm}\not\equiv \mp \infty$ on $D$,…
We consider Bergman spaces and variations of them in one or several complex variables. For some domains we show that in these spaces the generic function is totally unbounded and hence non - extendable. We also show that the generic…
The paper describes ergodic (with respect to the Haar measure) functions in the class of all functions, which are defined on (and take values in) the ring of p-adic integers, and which satisfy (at least, locally) Lipschitz condition with…
In this paper, we analyze the theory of meromorphic $(1,0)$-forms $\omega\in\mathcal{M}\Omega^{(1,0)}(\mathbb{CP}^1).$ Hence, we show that on a compact Riemann surface of genus $g=0,$ isomorphic to $\mathbb{CP}^1,$ every non-constant…
A study is made, of families of Hamiltonians parameterized over open subsets of Banach spaces in a way which renders many interesting properties of eigenstates and thermal states analytic functions of the parameter. Examples of such…
In classical function theory, a function is holomorphic if and only if it is complex analytic. For higher dimensional spaces it is natural to work in the context of Clifford algebras. The structures of these algebras depend on the parity of…
In this paper, we prove Huang et al.'s conjecture stated that if $f$ is a holomorphic function on $\Delta^+:=\{z\in \mathbb C \colon |z|<1,~\mathrm{Im}(z)>0\}$ with $\mathcal{C}^\infty$-smooth extension up to $(-1,1)$ such that $f$ maps…
We prove the existence of rotational hypersurfaces in $\mathbb{H}^n\times \mathbb{R}$ with $H_{r+1}=0$ and we classify them. Then we prove some uniqueness theorems for $r$-minimal hypersurfaces with a given (finite or asymptotic) boundary.…
We study linear and algebraic structures in sets of bounded holomorphic functions on the ball which have large cluster sets at every possible point (i.e., every point on the sphere in several complex variables and every point of the closed…
In this thesis we solve the coboundary equation $\delta c=d$ with bounds for cochains with values in a coherent subsheaf of some $\mathcal{O}^p_{\Omega}$, where $\Omega$ is a Stein manifold. In particular the existence of a finite set of…
Let $R^h$ denote the polynomial ring in variables $x_1,\,\ldots,\, x_h$ over a specified field $K$. We consider all of these rings simultaneously, and in each use lexicographic (lex) monomial order with $x_1 > \cdots > x_h$. Given a fixed…
The Monodromy Conjecture asserts that if c is a pole of the local topological zeta function of a hypersurface, then exp(2\pi i c) is an eigenvalue of the monodromy on the cohomology of the Milnor fiber. A stronger version of the conjecture…
We study an irreducible real-analytic germ of an $n$-dimensional variety in $n$ dimensional complex space. Assuming that the variety is Segre nondegenerate we define an averaging operator that generalizes the Moser--Webster involution. This…
In this paper we show that a holomorphic function, defined on an open subset $D$ of $\mathbb{C}^n$, is a complex Nash function if and only if its real part (or equivalently its imaginary part) is a real Nash function.
In this article, we prove a normality criterion for a family of meromorphic functions having zeros with some multiplicity which involves sharing of a holomorphic function by the members of the family. Our result generalizes Montel's…
Let $B(\Omega)$ be the Banach space of holomorphic functions on a bounded connected domain $\Omega$ in $\mathbb C^n$, which contains the ring of polynomials on $\Omega $. In this paper, we first establish a criterion for $B(\Omega )$ to be…
We give analytic and algebraic conditions under which a deformation of real analytic functions with non-isolated singular locus is a deformation with fibre constancy.
We study functions from a unique factorization monoid to a field. The set of all such functions is a commutative ring isomorphic to a ring of formal power series over the field, with indeterminates indexed by the prime elements of the…
Given a family of analytic functions near 0 \in C^n parametrized by a smooth space, we study the Bernstein polynomial of the fiber on an irreducible variety V of the space of parameters and we show that it is generically constant. We prove…