Szego Kernel Asymptotics For High Power Of Cr Line Bundles And Kodaira Embedding Theorems On Cr Manifolds
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Szego Kernel Asymptotics For High Power Of Cr Line Bundles And Kodaira Embedding Theorems On Cr Manifolds
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Author : Chin-Yu Hsiao
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-09
Szego Kernel Asymptotics For High Power Of Cr Line Bundles And Kodaira Embedding Theorems On Cr Manifolds written by Chin-Yu Hsiao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-09 with Mathematics categories.
Let X be an abstract not necessarily compact orientable CR manifold of dimension 2n−1, n⩾2, and let Lk be the k-th tensor power of a CR complex line bundle L over X. Given q∈{0,1,…,n−1}, let □(q)b,k be the Gaffney extension of Kohn Laplacian for (0,q) forms with values in Lk. For λ≥0, let Π(q)k,≤λ:=E((−∞,λ]), where E denotes the spectral measure of □(q)b,k. In this work, the author proves that Π(q)k,≤k−N0F∗k, FkΠ(q)k,≤k−N0F∗k, N0≥1, admit asymptotic expansions with respect to k on the non-degenerate part of the characteristic manifold of □(q)b,k, where Fk is some kind of microlocal cut-off function. Moreover, we show that FkΠ(q)k,≤0F∗k admits a full asymptotic expansion with respect to k if □(q)b,k has small spectral gap property with respect to Fk and Π(q)k,≤0 is k-negligible away the diagonal with respect to Fk. By using these asymptotics, the authors establish almost Kodaira embedding theorems on CR manifolds and Kodaira embedding theorems on CR manifolds with transversal CR S1 action.
Szeg Kernel Asymptotics For High Power Of Cr Line Bundles And Kodaira Embedding Theorems On Cr Manifolds
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Author : Chin-Yu Hsiao
language : en
Publisher:
Release Date : 2018
Szeg Kernel Asymptotics For High Power Of Cr Line Bundles And Kodaira Embedding Theorems On Cr Manifolds written by Chin-Yu Hsiao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Holomorphic Morse Inequalities And Bergman Kernels
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Author : Xiaonan Ma
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-14
Holomorphic Morse Inequalities And Bergman Kernels written by Xiaonan Ma and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-14 with Mathematics categories.
This book examines holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel. It opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are also included, such as an analytic proof of Kodaira's embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, compactification of complete Kähler manifolds of pinched negative curvature, Berezin-Toeplitz quantization, weak Lefschetz theorems, and asymptotics of the Ray-Singer analytic torsion.
Coherent Analytic Sheaves
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Author : H. Grauert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Coherent Analytic Sheaves written by H. Grauert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
... Je mehr ich tiber die Principien der Functionentheorie nachdenke - und ich thue dies unablassig -, urn so fester wird meine Uberzeugung, dass diese auf dem Fundamente algebraischer Wahrheiten aufgebaut werden muss (WEIERSTRASS, Glaubensbekenntnis 1875, Math. Werke II, p. 235). 1. Sheaf Theory is a general tool for handling questions which involve local solutions and global patching. "La notion de faisceau s'introduit parce qu'il s'agit de passer de donnees 'locales' a l'etude de proprietes 'globales'" [CAR], p. 622. The methods of sheaf theory are algebraic. The notion of a sheaf was first introduced in 1946 by J. LERAY in a short note Eanneau d'homologie d'une representation, C.R. Acad. Sci. 222, 1366-68. Of course sheaves had occurred implicitly much earlier in mathematics. The "Monogene analytische Functionen", which K. WEIERSTRASS glued together from "Func tionselemente durch analytische Fortsetzung", are simply the connected components of the sheaf of germs of holomorphic functions on a RIEMANN surface*'; and the "ideaux de domaines indetermines", basic in the work of K. OKA since 1948 (cf. [OKA], p. 84, 107), are just sheaves of ideals of germs of holomorphic functions. Highly original contributions to mathematics are usually not appreciated at first. Fortunately H. CARTAN immediately realized the great importance of LERAY'S new abstract concept of a sheaf. In the polycopied notes of his Semina ire at the E.N.S
L2 Approaches In Several Complex Variables
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Author : Takeo Ohsawa
language : en
Publisher: Springer
Release Date : 2018-11-28
L2 Approaches In Several Complex Variables written by Takeo Ohsawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Mathematics categories.
This monograph presents the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Special emphasis is put on the new precise results on the L2 extension of holomorphic functions in the past 5 years.In Chapter 1, the classical questions of several complex variables motivating the development of this field are reviewed after necessary preparations from the basic notions of those variables and of complex manifolds such as holomorphic functions, pseudoconvexity, differential forms, and cohomology. In Chapter 2, the L2 method of solving the d-bar equation is presented emphasizing its differential geometric aspect. In Chapter 3, a refinement of the Oka–Cartan theory is given by this method. The L2 extension theorem with an optimal constant is included, obtained recently by Z. Błocki and separately by Q.-A. Guan and X.-Y. Zhou. In Chapter 4, various results on the Bergman kernel are presented, including recent works of Maitani–Yamaguchi, Berndtsson, Guan–Zhou, and Berndtsson–Lempert. Most of these results are obtained by the L2 method. In the last chapter, rather specific results are discussed on the existence and classification of certain holomorphic foliations and Levi flat hypersurfaces as their stables sets. These are also applications of the L2 method obtained during the past 15 years.
An Introduction To Cr Structures
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Author : Howard Jacobowitz
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
An Introduction To Cr Structures written by Howard Jacobowitz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
The geometry and analysis of CR manifolds is the subject of this expository work, which presents all the basic results on this topic, including results from the folklore of the subject.
Cr Manifolds And The Tangential Cauchy Riemann Complex
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Author : Al Boggess
language : en
Publisher: CRC Press
Release Date : 1991-09-12
Cr Manifolds And The Tangential Cauchy Riemann Complex written by Al Boggess and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-09-12 with Mathematics categories.
CR Manifolds and the Tangential Cauchy Riemann Complex provides an elementary introduction to CR manifolds and the tangential Cauchy-Riemann Complex and presents some of the most important recent developments in the field. The first half of the book covers the basic definitions and background material concerning CR manifolds, CR functions, the tangential Cauchy-Riemann Complex and the Levi form. The second half of the book is devoted to two significant areas of current research. The first area is the holomorphic extension of CR functions. Both the analytic disc approach and the Fourier transform approach to this problem are presented. The second area of research is the integral kernal approach to the solvability of the tangential Cauchy-Riemann Complex. CR Manifolds and the Tangential Cauchy Riemann Complex will interest students and researchers in the field of several complex variable and partial differential equations.
Complex Manifolds And Deformation Of Complex Structures
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Author : K. Kodaira
language : en
Publisher: Springer Science & Business Media
Release Date : 1985-11-22
Complex Manifolds And Deformation Of Complex Structures written by K. Kodaira and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-11-22 with Mathematics categories.
Heat Kernels And Dirac Operators
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Author : Nicole Berline
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-12-08
Heat Kernels And Dirac Operators written by Nicole Berline and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-08 with Mathematics categories.
In the first edition of this book, simple proofs of the Atiyah-Singer Index Theorem for Dirac operators on compact Riemannian manifolds and its generalizations (due to the authors and J.-M. Bismut) were presented, using an explicit geometric construction of the heat kernel of a generalized Dirac operator; the new edition makes this popular book available to students and researchers in an attractive paperback.
Boltzmann S Legacy
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Author : Jakob Yngvason
language : en
Publisher: European Mathematical Society
Release Date : 2008
Boltzmann S Legacy written by Jakob Yngvason and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Biography & Autobiography categories.
Ludwig Eduard Boltzmann (1844-1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. He was one of the most important advocates for atomic theory when that scientific model was still highly controversial. To commemorate the 100th anniversary of his death in Duino, the International Symposium ``Boltzmann's Legacy'' was held at the Erwin Schrodinger International Institute for Mathematical Physics in June 2006. This text covers a broad spectrum of topics ranging from equilibrium statistical and nonequilibrium statistical physics, ergodic theory and chaos to basic questions of biology and historical accounts of Boltzmann's work. Besides the lectures presented at the symposium the volume also contains contributions specially written for this occasion. The articles give a broad overview of Boltzmann's legacy to the sciences from the standpoint of some of today's leading scholars in the field. The book addresses students and researchers in mathematics, physics, and the history of science.