Related papers: Boundary cross theorem in dimension 1 with singula…

Let $M$ be a subharmonic function with Riesz measure $\nu_M$ in a domain $D$ in the $n$-dimensional complex Euclidean space $\mathbb C^n$, and let $f$ be a nonzero function that is holomorphic in $D$, vanishes on a set ${\sf Z}\subset D$,…

It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…

We study the structure of the spectrum of the algebra of uniformly continuous holomorphic functions on the unit ball of $\ell_p$. Our main focus is the relationship between \emph{Gleason parts} and \emph{fibers}. For every $z \in…

We show in this paper that every domain in a separable Hilbert space, say $\cH$, which has a $C^2$ smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of $\cH$. This is…

We study various manifestations of structural crossover in the properties of a binary mixture of hard-spheres. For homogeneous mixtures that are sufficiently asymmetric, there is a crossover line in the phase diagram such that for…

Let $X$ be a connected, compact complex manifold and $S\subset X$ a separating real hypersurface, so that $X$ decomposes as a union of compact complex manifolds with boundary $\bar X^\pm$. Let $\mathcal{M}$ be the moduli space of $S$-framed…

We prove that if a positive closed current is bounded by another one with bounded, continuous or Hoelder continuous super-potentials, then it inherits the same property. There are two different methods to define wedge-products of positive…

The aim of the article is an extension of the Monodromy Conjecture of Denef and Loeser in dimension two, incorporating zeta functions with differential forms and targeting all monodromy eigenvalues, and also considering singular ambient…

We prove that the linearization of a germ of holomorphic map of the type $F_\lambda(z)=\lambda(z+O(z^2))$ has a $ C^1$--holomorphic dependence on the multiplier $\lambda$. $C^1$--holomorphic functions are $ C^1$--Whitney smooth functions,…

Consider a continuous one parameter family of circles in complex plane that contains two circles lying in the exterior of one another. Under mild assumptions on the family, we prove that if a continuous function on the union of the above…

Let $D$ be a domain in the complex plane, $M$ be an extended real function on $D$. If $f$ is a non-zero holomorphic function on $D$ with an upper constraint $|f|\leq \exp M$ on this domain $D$, then it is natural to expect that there must…

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…

We prove that a proper holomorphic map between two bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomorphism. Our methods allow us to give a single, all-encompassing argument that unifies the…

Let $f: M \to M$ be a diffeomorphism defined on a compact boundaryless $d$-dimensional manifold $M$, $d\geq 2$. C. Morales has proposed the notion of measure expansiveness. In this note we show that diffeomorphisms in a residual subset far…

It is shown that certain diffeomorphism or homeomorphism groups with no restriction on support of an open manifold with finite number of ends are bounded. It follows that these groups are uniformly perfect. In order to characterize the…

We describe bounded, holomorphic functions on the complex 2-disc, that admit meromorphic extension to a larger 2-disc. This solves a conjecture of Bickel, Knese, Pascoe and Sola. The key technical ingredient is an old theorem of Zariski…

Let $f: M \to M$ denote a diffeomorphism of a smooth manifold $M$. Let $p$ in $M$ be its hyperbolic fixed point with stable and unstable manifolds $W_S$ and $W_U$, respectively. Assume that $W_S$ is a curve. Suppose that $W_U$ and $W_S$…

We deal with the distributions of holomorphic curves and integral points off divisors. We will simultaneouly prove an optimal dimension estimate from above of a subvariety W off a divisor D which contains a Zariski dense entire holomorphic…

The present paper studies a quantitative version of the transversality theorem. More precisely, given a continuous function $f\in \mathcal{C}([0,1]^d,\mathbb{R}^m)$ and a manifold $W\subset \mathbb{R}^m$ of dimension $p$, a sharpness result…

Employing Morse theory for the global control of monodromy and the method of analytic discs for local extension, we establish a version of the global Hartogs extension theorem in a singular setting: for every domain D of an (n-1)-complete…