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The Complex Monge Amp Re Equation And Pluripotential Theory


The Complex Monge Amp Re Equation And Pluripotential Theory
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The Complex Monge Amp Re Equation And Pluripotential Theory


The Complex Monge Amp Re Equation And Pluripotential Theory
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Author : Sławomir Kołodziej
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

The Complex Monge Amp Re Equation And Pluripotential Theory written by Sławomir Kołodziej 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 2005 with Mathematics categories.


This is a collection of results on the existence and stability of weak solutions of complex Monge-Ampere equation proved by applying pluripotential theory methods and obtained in past three decades. Firstly introducing basic concepts and theorems of pluripotential theory, then the Dirichlet problem for the complex Monge-Ampere equation is studied. The main goal is to give possibly detailed description of the nonnegative Borel measures which on the right hand side of the equation give rise to plurisubharmonic solutions satisfying additional requirements such as continuity, boundedness or some weaker ones. In the last part the methods of pluripotential theory are implemented to prove the existence and stability of weak solutions of the complex Monge-Ampere equation on compact Kahler manifolds. This is a generalization of the Calabi-Yau theorem.



The Complex Monge Ampere Equation And Pluripotential Theory


The Complex Monge Ampere Equation And Pluripotential Theory
DOWNLOAD
Author : Sławomir Kołodziej
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

The Complex Monge Ampere Equation And Pluripotential Theory written by Sławomir Kołodziej 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 2005 with Mathematics categories.


We collect here results on the existence and stability of weak solutions of complex Monge-Ampere equation proved by applying pluripotential theory methods and obtained in past three decades. First we set the stage introducing basic concepts and theorems of pluripotential theory. Then the Dirichlet problem for the complex Monge-Ampere equation is studied. The main goal is to give possibly detailed description of the nonnegative Borel measures which on the right hand side of the equation give rise to plurisubharmonic solutions satisfying additional requirements such as continuity, boundedness or some weaker ones. In the last part, the methods of pluripotential theory are implemented to prove the existence and stability of weak solutions of the complex Monge-Ampere equation on compact Kahler manifolds. This is a generalization of the Calabi-Yau theorem.



Pluripotential Theory


Pluripotential Theory
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Author : Giorgio Patrizio
language : en
Publisher: Springer
Release Date : 2013-05-16

Pluripotential Theory written by Giorgio Patrizio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-16 with Mathematics categories.


Pluripotential theory is a very powerful tool in geometry, complex analysis and dynamics. This volume brings together the lectures held at the 2011 CIME session on "pluripotential theory" in Cetraro, Italy. This CIME course focused on complex Monge-Ampére equations, applications of pluripotential theory to Kahler geometry and algebraic geometry and to holomorphic dynamics. The contributions provide an extensive description of the theory and its very recent developments, starting from basic introductory materials and concluding with open questions in current research.



Pluripotential Theory


Pluripotential Theory
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Author : Maciej Klimek
language : en
Publisher:
Release Date : 1991

Pluripotential Theory written by Maciej Klimek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.


Pluripotential theory is a recently developed non-linear complex counterpart of classical potential theory. Its main area of application is multidimensional complex analysis. The central part of the pluripotential theory is occupied by maximal plurisubharmonic functions and the generalized complex Monge-Ampere operator. The interplay between these two notions provides the focal point of this monography, which contains an account of the developments from the large volume of recent work in this area. The substantial proportion of this volume devoted to classical properties of subharmonic and plurisubharmonic functions makes the pluripotential theory available to a wide audience of analysts.



Pluripotential Theory


Pluripotential Theory
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Author : Maciej Klimek
language : en
Publisher:
Release Date : 2023

Pluripotential Theory written by Maciej Klimek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Functions of several complex variables categories.


This monograph presents a recently developed branch of analysis in several complex variables. It focuses on the interplay between maximal plurisubharmonic functions and the generalized complex Monge-Ampere operator.



Entire Functions Of Several Complex Variables


Entire Functions Of Several Complex Variables
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Author : Pierre Lelong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Entire Functions Of Several Complex Variables written by Pierre Lelong 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.


I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions.



Explorations In Harmonic Analysis


Explorations In Harmonic Analysis
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Author : Steven G. Krantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-24

Explorations In Harmonic Analysis written by Steven G. Krantz 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 2009-05-24 with Mathematics categories.


This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.



Potential Theory In The Complex Plane


Potential Theory In The Complex Plane
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Author : Thomas Ransford
language : en
Publisher: Cambridge University Press
Release Date : 1995-03-16

Potential Theory In The Complex Plane written by Thomas Ransford and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-16 with Mathematics categories.


Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions.



Bollettino Della Unione Matematica Italiana


Bollettino Della Unione Matematica Italiana
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Author : Unione matematica italiana
language : en
Publisher:
Release Date : 2005

Bollettino Della Unione Matematica Italiana written by Unione matematica italiana and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.




Degenerate Complex Monge Amp Re Equations


Degenerate Complex Monge Amp Re Equations
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Author : Vincent Guedj
language : en
Publisher:
Release Date :

Degenerate Complex Monge Amp Re Equations written by Vincent Guedj and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.