Holomorphic horospherical duality "sphere-cone"
英文摘要:
We describe a construction of complex geometrical analysis which corresponds to the classical theory of spherical harmonics.
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Simon Gindikin
We describe a construction of complex geometrical analysis which corresponds to the classical theory of spherical harmonics.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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It is proved that CR functions on a quadratic cone M in $\C^n$, n>1, admit one-sided holomorphic extension if and only if M does not have two-sided support, a geometric condition on M which generalizes minimality in the sense of Tumanov. A biholomorphic classification of quadratic cones in $\C^2$ is also given.
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Holomorphic approximation by polynomials with exponents restricted to a convex cone
该文研究指数限制在凸锥上的多项式对多复变量全纯函数的逼近,证明了对应版本的Runge-Oka-Weil定理,在旋转对称紧集上得到更精细结果,并给出相关Siciak-Zakharyuta函数的表达式。
In this paper we investigate the global behavior of proper holomorphic maps f from the unit disc U={|z|<1} to C^2. The fact that U is transcendental imposes certain restrictions on the image f(U). For instance, f(U) cannot be contained in any proper complex cone in C^2 since this would force it to be algebraic. On the other hand, we show that a real cone in C^2 with axis R^2 contains the image of a proper holomorphic map f from U to C^2 if and only if the angle of the cone is larger than pi/2. We also construct maps f as above whose images avoid both coordinate axes in C^2. Equivalently, we co…
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On CR maps from the sphere into the tube over the future light cone II: Higher dimensions
本研究确定了三维复空间中球面到四维未来光锥管域的所有CR映射,完整刻画三维单位球到四维第四类典型域的逆紧全纯映射并证实Reiter-Son猜想,还证明任意维下球到第四类典型域等距全纯嵌入的边界刻画并用于处理一般刻画的特殊情形。
We show that expanding Kähler-Ricci solitons which have positive holomorphic bisectional curvature and are asymptotic to Kähler cones at infinity must be the U(n)-rotationally symmetric expanding solitons constructed by Cao.
Holomorphic and Formal First Integrals for Foliations of Codimension One on Complex Analytic Space Germs
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We determine all local smooth or formal CR maps from the unit sphere $\mathbb{S}^3\subset \mathbb{C}^2$ into the tube $\mathcal{T}:= \mathcal{C} \times i\mathbb{R}^3 \subset \mathbb{C}^3$ over the future light cone $\mathcal{C}:= \left\{x\in \mathbb{R}^3\colon x_1^2+x_2^2 = x_3^2, \ x_3 > 0\right\}$. This result leads to a complete classification of proper holomorphic maps from the unit ball in $\mathbb{C}^2$ into Cartan's classical domain of type IV in $\mathbb{C}^3$ that extend smoothly to some boundary point. Up to composing with CR automorphisms of the source and target, the classification…
Weak slice regular functions on the $n$-dimensional quadratic cone of octonions
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This paper is intended as the first step of a programme aiming to prove in the long run the long-conjectured closedness under holomorphic deformations of compact complex manifolds that are bimeromorphically equivalent to compact Kähler manifolds, known as Fujiki {\it class} ${\cal C}$ manifolds. Our main idea is to explore the link between the {\it class} ${\cal C}$ property and the closed positive currents of bidegree $(1,\,1)$ that the manifold supports, a fact leading to the study of semi-continuity properties under deformations of the complex structure of the dual cones of cohomology class…
Let $X$ be a complex manifold and $S\hookrightarrow X$ be an embedding of complex submanifold. Assuming that the embedding is $(k-1)$-linearizable or $(k-1)$-comfortably embedded, we construct via the deformation to the normal cone a diffeomorphism $F$ from a small neighborhood of the zero section in the normal bundle $N_{S}$ to a small neighborhood of $S$ in $X$ such that $F$ is in a precise sense holomorphic to the $(k-1)$-th order. Using this $F$ we obtain optimal estimates on asymptotical rates for asymptotically conical Calabi-Yau metrics constructed by Tian-Yau. Furthermore, when $S$ is …
Let f be a holomorphic automorphism of a compact Kahler manifold (X,ω) of dimension k>1. We study the convex cones of positive closed (p,p)-currents T_p, which satisfy a functional relation $f^*(T_p)=λT_p, λ>1,$ and some regularity condition (PB). Under appropriate assumptions on dynamical degrees we introduce closed finite dimensional cones, not reduced to zero, of such currents. In particular, when the topological entropy h(f) of f is positive, then for some m, there is a positive closed (m,m)-current T_m which satisfies the relation $f^* T_m=\exp(h(f)) T_m$. Moreover,every quasi-p.s.h. func…
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