Holomorphicity

Mục đích của bài luận văn là nghiên cứu một số tính chất của lớp các hàm số triệt tiêu cấp vô hạn và ứng dụng của chúng trong bài toán về sự tồn tại trường vectơ chỉnh hình tiếp xúc. Luận văn trình bày lại một số kết quả trong bài báo “A note on uniqueness boundary of holomorphic mappings” của các tác giả Ninh Văn Thu, Nguyễn Ngọc Khanh và tiền ấn phẩm “On the nonexistence of nontrivial tangential holomorphic vector fields of a certain hypersurface of infinite type” của tác giả Ninh Văn Thu.

28p capheviahe26 02-02-2021 24 2   Download

The notions of hyperbolicity and tautness modulo an analytic subset of complex spaces are due to S. Kobayashi. Much attention has been given to these notions, and the results on this problem can be applied to many areas of mathematics, in particular to the extensions of holomorphic mappings. The main goal of this article is to give necessary and sufficient conditions on the hyperbolicity or tautness modulo an analytic subset of complex spaces.

10p tamynhan5 10-12-2020 12 2   Download

In this paper, we establish a second main theorem for holomorphic mappings from a disc (R) into Pn(C) and families of hyperplanes in subgeneral position. Our result is an extension the classical second main theorem of Cartan-Nochka and the second main theorem of Fujimoto.

9p tamynhan9 02-12-2020 10 3   Download

Let X be a compact K¨hler manifold with strictly pseudoconvex bounda ary, Y. In this setting, the SpinC Dirac operator is canonically identified with ¯ ¯ ∂ + ∂ ∗ : C ∞ (X; Λ0,e ) → C ∞ (X; Λ0,o ). We consider modifications of the classi¯ cal ∂-Neumann conditions that define Fredholm problems for the SpinC Dirac operator. In Part 2, [7], we use boundary layer methods to obtain subelliptic estimates for these boundary value problems. Using these results, we obtain an expression for the finite part of the holomorphic Euler characteristic of a strictly pseudoconvex manifold...

33p noel_noel 17-01-2013 42 5   Download

Annals of Mathematics By Curtis T. McMullen* .Annals of Mathematics, 165 (2007), 397–456 Dynamics of SL2(R) over moduli space in genus two By Curtis T. McMullen* Abstract This paper classifies orbit closures and invariant measures for the natural action of SL2 (R) on ΩM2 , the bundle of holomorphic 1-forms over the moduli space of Riemann surfaces of genus two. Contents 1. Introduction 2. Dynamics and Lie groups 3. Riemann surfaces and holomorphic 1-forms 4. Abelian varieties with real multiplication 5. Recognizing eigenforms 6. Algebraic sums of 1-forms 7. Connected sums of 1-forms 8.

61p noel_noel 17-01-2013 54 6   Download

Given a holomorphic vector bundle E over a compact K¨hler manifold X, a one defines twisted Gromov-Witten invariants of X to be intersection numbers in moduli spaces of stable maps f : Σ → X with the cap product of the virtual fundamental class and a chosen multiplicative invertible characteristic class of the virtual vector bundle H 0 (Σ, f ∗ E) H 1 (Σ, f ∗ E). Using the formalism of quantized quadratic Hamiltonians [25], we express the descendant potential for the twisted theory in terms of that for X. ...

40p noel_noel 17-01-2013 57 7   Download

The purpose of this paper is to carry out the abelianization program proposed by Atiyah [1] and Hitchin [9] for the geometric quantization of SU(2) Wess-Zumino-Witten model. Let C be a Riemann surface of genus g. Let Mg be the moduli space of semi-stable rank 2 holomorphic vector bundles on C with trivial determinant. For a positive integer k, let Γ(Mg , Lk ) be the space of holomorphic sections of the k-th tensor product of the determinant line bundle L on Mg . An element of Γ(Mg , Lk ) is called a rank 2 theta function...

50p noel_noel 17-01-2013 60 8   Download

To Bidisha and Ananya Abstract We prove integrality of the ratio f, f / g, g (outside an explicit finite set of primes), where g is an arithmetically normalized holomorphic newform on a Shimura curve, f is a normalized Hecke eigenform on GL(2) with the same Hecke eigenvalues as g and , denotes the Petersson inner product. The primes dividing this ratio are shown to be closely related to certain level-lowering congruences satisfied by f and to the central values of a family of Rankin-Selberg L-functions. Finally we give two applications, the first to proving the integrality of a...

68p noel_noel 17-01-2013 54 6   Download

We prove that the classical Oka property of a complex manifold Y, concerning the existence and homotopy classification of holomorphic mappings from Stein manifolds to Y, is equivalent to a Runge approximation property for holomorphic maps from compact convex sets in Euclidean spaces to Y . Introduction Motivated by the seminal works of Oka [40] and Grauert ([24], [25], [26]) we say that a complex manifold Y enjoys the Oka property if for every Stein manifold X, every compact O(X)-convex subset K of X and every continuous map f0 : X → Y which is holomorphic in an...

20p noel_noel 17-01-2013 52 5   Download

We prove that any genus-2 Lefschetz fibration without reducible fibers and with “transitive monodromy” is holomorphic. The latter condition comprises all cases where the number of singular fibers µ ∈ 10N is not congruent to 0 modulo 40. This proves a conjecture of the authors in [SiTi1]. An auxiliary statement of independent interest is the holomorphicity of symplectic surfaces in S 2 -bundles over S 2 , of relative degree ≤ 7 over the base, and of symplectic surfaces in CP2 of degree ≤ 17. ...

63p noel_noel 17-01-2013 47 5   Download

In [27], we introduced Floer homology theories HF − (Y, s), HF ∞ (Y, s), HF (Y, s),and HFred (Y, s) associated to closed, oriented three-manifolds Y equipped with a Spinc structures s ∈ Spinc (Y ). In the present paper, we give calculations and study the properties of these invariants. The calculations suggest a conjectured relationship with Seiberg-Witten theory.

88p tuanloccuoi 04-01-2013 55 6   Download

Holomorphic disks and topological invariants for closed three-manifolds ´ ´ ´ By Peter Ozsvath and Zoltan Szabo* Abstract The aim of this article is to introduce certain topological invariants for closed, oriented three-manifolds Y , equipped with a Spinc structure. Given a Heegaard splitting of Y = U0 ∪Σ U1 , these theories are variants of the Lagrangian Floer homology for the g-fold symmetric product of Σ relative to certain totally real subspaces associated to U0 and U1 . 1. Introduction Let Y be a connected, closed, oriented three-manifold, equipped with a Spin structure s. ...

133p tuanloccuoi 04-01-2013 51 7   Download

In the symplectic category there is a ‘connect sum’ operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds. This paper establishes a formula for the Gromov-Witten invariants of a symplectic sum Z = X#Y in terms of the relative GW invariants of X and Y . Several applications to enumerative geometry are given. Gromov-Witten invariants are counts of holomorphic maps into symplectic manifolds.

92p tuanloccuoi 04-01-2013 44 7   Download

The usual index theorems for holomorphic self-maps, like for instance the classical holomorphic Lefschetz theorem (see, e.g., [GH]), assume that the fixed-points set contains only isolated points. The aim of this paper, on the contrary, is to prove index theorems for holomorphic self-maps having a positive dimensional fixed-points set. The origin of our interest in this problem lies in holomorphic dynamics.

47p tuanloccuoi 04-01-2013 49 6   Download

Let G be a connected, real, semisimple Lie group contained in its complexification GC , and let K be a maximal compact subgroup of G. We construct a KC -G double coset domain in GC , and we show that the action of G on the K-finite vectors of any irreducible unitary representation of G has a holomorphic extension to this domain. For the resultant holomorphic extension of K-finite matrix coefficients we obtain estimates of the singularities at the boundary, as well as majorant/minorant estimates along the boundary. ...

85p tuanloccuoi 04-01-2013 48 7   Download

A basic result in the theory of holomorphic functions of several complex variables is the following special case of the work of H. Cartan on the sheaf cohomology on Stein domains ([10], or see [14] or [16] for more modern treatments). Theorem 1.1. If V is an analytic variety in a domain of holomorphy Ω and if f is a holomorphic function on V , then there is a holomorphic function g in Ω such that g = f on V . The subject of this paper concerns an add-on to the structure considered in Theorem 1.1 which...

25p tuanloccuoi 04-01-2013 51 5   Download

Đối với các chức năng hài hòa và riêng biệt hòa, chúng tôi cho kết quả tương tự như định lý Carlson-Boas. Chúng tôi cung cấp cho hài hòa tương tự như các định lý Polya và Guelfond.1. Giới thiệu cũng được biết đến định lý cổ điển của Carlson (xem [2, p.153]) nói rằng một holomorphic toàn bộ chức năng của loại theo cấp số nhân.

6p phalinh21 01-09-2011 44 3   Download

Trong bài báo này, khái niệm về không gian và không gian Forelli Hartogs được đưa ra. Bất biến của không gian Hartogs và Forelli thông qua các tấm phủ holomorphic được thành lập. Hơn nữa, theo các giả định trên hlerity holomorphically lồi ¨ K, chúng tôi cho thấy ba loại sau đây của các không gian phức tạp: Hartogs mở rộng không gian holomorphic, không gian Hartogs và không gian có tài sản Forelli trùng.

11p phalinh21 01-09-2011 55 4   Download

ông nhằm mục đích của bài viết này là để cho một số kết quả về mối quan hệ giữa pluripolarity của đồ thị và holomorphicity các chức năng phức tạp có giá trị. Đặc biệt, chúng tôi điều tra mối quan hệ giữa pluripolarity của đồ thị và holomorphicity của Hartogs loại và loại Forelli.

10p phalinh21 01-09-2011 47 4   Download

là polydiscs đơn vị Cn, φ (z) = (φ1 (z ),..., φn (z)) là một holomorphic tự bản đồ của D và ψ (z) một chức năng holomorphic trên Dn. Các điều kiện cần và đủ được thiết lập cho ψCφ nhà điều hành thành phần trọng gây ra bởi φ (z) và ψ (z) được giới hạn hoặc nhỏ gọn giữa các không gian khác nhau trọng Bergman trong polydiscs.

10p phalinh21 01-09-2011 58 4   Download