相关论文: On the reflection principle in C^n
The main purpose of this article is to present a generalization of Forelli's theorem for the functions holomorphic along a general pencil of holomorphic discs. This generalizes the main result of \cite{JKS13} and the original Forelli's…
We give a modular branching rule for certain wreath products as a generalization of Kleshchev's modular branching rule for the symmetric groups. Our result contains a modular branching rule for the complex reflection groups $G(m,1,n)$…
We introduce the concept of spherical (as distinguished from planar) reflection positivity and use it to obtain a new proof of the sharp constants in certain cases of the HLS and the logarithmic HLS inequality. Our proofs relies on an…
Given a point S and any irreducible algebraic curve C in P^2 (with any type of singularities), we consider the caustic of reflection defined as the Zariski closure of the envelope of the reflected lines from the point S on the curve C. We…
We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space…
We prove a $C^\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces. This is a consequence of a $C^\infty$ closing lemma for Reeb flows on closed contact three-manifolds, which was recently proved as an application of…
In this paper we present the notion of a von Neumann regular $\mathcal{C}^{\infty}-$ring, we prove some results about them and we describe some of their properties. We prove, using two different methods, that the category of von Neumann…
We consider boundary conditions compatible with discrete holomorphicity for the dilute O(n) and C_2^(1) loop models. In each model, for a general set of boundary plaquettes, multiple types of loops can appear. A generalisation of Smirnov's…
We investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities. We give a simple necessary and sufficient…
The purpose of this article is to show a second main theorem with the explicit truncation level for holomorphic mappings of $ \mathbb{C} $ (or of a compact Riemann surface) into a compact complex manifold sharing divisors in subgeneral…
We introduce a model to design reflectors that take into account the inverse square law for radiation. We prove existence of solutions, both in the near and far field cases, when the input and output energies are prescribed.
R. Guralnick (Linear Algebra Appl. 99, 85-96, 1988) proved that two holomorphic matrices on a noncompact connected Riemann surface, which are locally holomorphically similar, are globally holomorphically similar. We generalize this to…
We describe representations of groupoid C*-algebras on Hilbert modules over arbitrary C*-algebras by a universal property. For Hilbert space representations, our universal property is equivalent to Renault's Integration-Disintegration…
The cosmic holographic principle suggested by Fischler and Susskind has been examined in (2+1)-dimensional cosmological models. Analogously to the (3+1)-dimensional counterpart, the holographic principle is satisfied in all flat and open…
It was argued recently that there exists an unexpected phenomenon, the reflection of incoming particles on the event horizon of black holes (Kuchiev(2003)). This means that a particle approaching the black hole can bounce back into the…
In this paper we study the cohomology of the de Rham complex of sheaves of reflexive differential forms on a normal complex space. First, we prove that the complex is exact in degree one under suitable conditions on the underlying…
In this paper, we prove a general version of Thomsen-Li's Theorem--a Krein-Milman type theorem for C*-algebras. To be precise, for a Markov operator on $C[0,1]$ which preserves certain subspace of $C[0,1]$, we approximate it by an average…
In this note we study several topics related to the schema of local reflection $\mathsf{Rfn}(T)$ and its partial and relativized variants. Firstly, we introduce the principle of uniform reflection with $\Sigma_n$-definable parameters,…
The aim of this paper is to give some applications of Zalcman's Rescalling Lemma.
Given a small category C, we show that there is a universal way of expanding C into a model category, essentially by formally adjoining homotopy colimits. The technique of localization becomes a method for imposing `relations' into these…