Related papers: Wermer type sets and extension of CR functions

Let $F$ be a global function field of characteristic $p>0$ and $A/F$ an abelian variety. Let $K/F$ be an $\l$-adic Lie extension ($\l\neq p$) unramified outside a finite set of primes $S$ and such that $\Gal(K/F)$ has no elements of order…

Let $F$ be an ordered topological vector space (over $\mathbb{R}$) whose positive cone $F_+$ is weakly closed, and let $E \subseteq F$ be a subspace. We prove that the set of positive continuous linear functionals on $E$ that can be…

Given a bounded strongly pseudoconvex domain $D$ in $\mathbb{C}^n$ with smooth boundary, we give a characterization through products of functions in weighted Bergman spaces of $(\lambda,\gamma)$-skew Carleson measures on $D$, with…

Wavelet sets that are finite unions of convex sets are constructed in $\mathbb R^n$, $n\geq 2$, for dilation by any expansive matrix that has a power equal to a scalar times the identity and also has all singular values greater than $\sqrt…

Let B be a thick spherical building equipped with its natural CAT(1) metric and let M be a proper, convex subset of B. If M is open or if M is a closed ball of radius pi/2, then the maximal subcomplex supported by the complement of M is…

In this paper, we build a compactification by a strictly pseudoconvex CR structure for complete and non-compact K\"ahler manifolds whose curvature tensor is asymptotic to that of the complex hyperbolic space.

This paper is concerned with the topological space of normalized quaternion-valued positive definite functions on an arbitrary abelian group G, especially its convex characteristics. There are two main results. Firstly, we prove that the…

We establish rigid tensor category structure on finitely-generated weight modules for the subregular $W$-algebras of $\mathfrak{sl}_n$ at levels $ - n + \frac{n}{n+1}$ (the $\mathcal{B}_{n+1}$-algebras of Creutzig-Ridout-Wood) and at levels…

For an open set $V\subset\mathbb{C}^n$, denote by $\mathscr{M}_{\alpha}(V)$ the family of $\alpha$-analytic functions that obey a boundary maximum modulus principle. We prove that, on a bounded domain $\Omega\subset \mathbb{C}^n$, with…

We prove the following theorem: let $\widetilde{\mathcal R}$ be an expansion of the real field $\overline{\mathbb R}$, such that every definable set (I) is a uniform countable union of semialgebraic sets, and (II) contains a "semialgebraic…

In $\C^2=\R^2+i\R^2$ with coordinates $z=(z_1,z_2), z=x+iy$, we consider a function $f$ continuous on a domain $\Omega$ of $\R^2$ separately real analytic in $x_1$ and CR extendible to $y_2$ (resp. CR extendible to $y_2>0$). This means that…

In this paper we give the first examples of positive closed currents in $\mathbb{C}^2$ with continuous potentials, vanishing self-intersection, and which are not laminar. More precisely, they are supported on sets "without analytic…

Let G be a connected, real, semisimple Lie group contained in its complexification G_C, and let K be a maximal compact subgroup of G. We construct a K_C-G double coset domain in G_C, and we show that the action of G on the K-finite vectors…

We prove some results on the density and multiplicity of positive solutions to the prescribed Webster scalar curvature problem on the $(2n+1)$-dimensional standard unit CR sphere $(\mathbb{S} ^{2n+1},\theta_0)$. Specifically, we construct…

In this paper we establish a gap theorem for the complex geometry of smoothly bounded convex domains which informally says that if the complex geometry near the boundary is close to the complex geometry of the unit ball, then the domain…

We construct a continuum of non-homeomorphic compact subspaces of the real line R without singleton components. Thus from the purely topological point of view the real line contains not only more closed sets than open sets but also more…

In this note we extend N. Th. Varopoulos result on zero sets of H p functions of strictly pseudo-convex domains in C n to lineally convex domains of finite type.

We prove that every smooth closed manifold admits a smooth real-valued function with only two critical values. We call a function of this type a \emph{Reeb function}. We prove that for a Reeb function we can prescribe the set of minima (or…

We get a new multiplicity result for gradient systems. Here is a very particular corollary: Let $\Omega\subset {\bf R}^n$ ($n\geq 2$) be a smooth bounded domain and let $\Phi:{\bf R}^2\to {\bf R}$ be a $C^1$ function, with $\Phi(0,0)=0$,…

Let $(M^{n+1},g)$ be a closed Riemannian manifold of dimension $3\le n+1\le 5$. We show that, if the metric $g$ is generic or if the metric $g$ has positive Ricci curvature, then $M$ contains infinitely many geometrically distinct constant…