Affine Bernstein Problems And Monge Amp Re Equations
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Affine Bernstein Problems And Monge Ampere Equations
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Author : An-Min Li
language : en
Publisher: World Scientific
Release Date : 2010
Affine Bernstein Problems And Monge Ampere Equations written by An-Min Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
In this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest. It gives a selfcontained introduction to research in the last decade concerning global problems in the theory of submanifolds, leading to some types of Monge-Amp re equations. From the methodical point of view, it introduces the solution of certain Monge-Amp re equations via geometric modeling techniques. Here geometric modeling means the appropriate choice of a normalization and its induced geometry on a hypersurface defined by a local strongly convex global graph. For a better understanding of the modeling techniques, the authors give a selfcontained summary of relative hypersurface theory, they derive important PDEs (e.g. affine spheres, affine maximal surfaces, and the affine constant mean curvature equation). Concerning modeling techniques, emphasis is on carefully structured proofs and exemplary comparisons between different modelings.
Handbook Of Geometric Analysis
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Author : Lizhen Ji
language : en
Publisher:
Release Date : 2008
Handbook Of Geometric Analysis written by Lizhen Ji and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
"Geometric Analysis combines differential equations with differential geometry. An important aspect of geometric analysis is to approach geometric problems by studying differential equations. Besides some known linear differential operators such as the Laplace operator, many differential equations arising from differential geometry are nonlinear. A particularly important example is the Monge-Amperè equation. Applications to geometric problems have also motivated new methods and techniques in differential equations. The field of geometric analysis is broad and has had many striking applications. This handbook of geometric analysis--the first of the two to be published in the ALM series--presents introductions and survey papers treating important topics in geometric analysis, with their applications to related fields. It can be used as a reference by graduate students and by researchers in related areas."--Back cover.
Journal F R Die Reine Und Angewandte Mathematik
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Author : August Leopold Crelle
language : en
Publisher:
Release Date : 2002
Journal F R Die Reine Und Angewandte Mathematik written by August Leopold Crelle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
An Introduction To Extremal Kahler Metrics
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Author : Gábor Székelyhidi
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-06-19
An Introduction To Extremal Kahler Metrics written by Gábor Székelyhidi 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 2014-06-19 with Mathematics categories.
A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kähler geometry. This book gives an introduction to the study of extremal Kähler metrics and in particular to the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry. The book addresses some of the basic ideas on both the analytic and the algebraic sides of this picture. An overview is given of much of the necessary background material, such as basic Kähler geometry, moment maps, and geometric invariant theory. Beyond the basic definitions and properties of extremal metrics, several highlights of the theory are discussed at a level accessible to graduate students: Yau's theorem on the existence of Kähler-Einstein metrics, the Bergman kernel expansion due to Tian, Donaldson's lower bound for the Calabi energy, and Arezzo-Pacard's existence theorem for constant scalar curvature Kähler metrics on blow-ups.
The Monge Amp Re Equation
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Author : Cristian E. Gutierrez
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-05-11
The Monge Amp Re Equation written by Cristian E. Gutierrez 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 2001-05-11 with Mathematics categories.
The Monge-Ampère equation has attracted considerable interest in recent years because of its important role in several areas of applied mathematics. Monge-Ampère type equations have applications in the areas of differential geometry, the calculus of variations, and several optimization problems, such as the Monge-Kantorovitch mass transfer problem. This book stresses the geometric aspects of this beautiful theory, using techniques from harmonic analysis – covering lemmas and set decompositions.
Geometry Iii
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Author : Yu.D. Burago
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Geometry Iii written by Yu.D. Burago 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 2013-03-14 with Mathematics categories.
The original version of this article was written more than fiveyears ago with S. Z. Shefel',a profound and original mathematician who died in 1984. Sincethen the geometry of surfaces has continued to be enriched with ideas and results. This has required changes and additions, but has not influenced the character of the article, the design ofwhich originated with Shefel'. Without knowing to what extent Shefel' would have approved the changes, I should nevertheless like to dedicate this article to his memory. (Yu. D. Burago) We are trying to state the qualitative questions of the theory of surfaces in Euclidean spaces in the form in which they appear to the authors at present. This description does not entirely correspond to the historical development of the subject. The theory of surfaces was developed in the first place mainly as the 3 theory of surfaces in three-dimensional Euclidean space E ; however, it makes sense to begin by considering surfaces F in Euclidean spaces of any dimension n~ 3. This approach enables us, in particular, to put in a new light some 3 unsolved problems of this developed (and in the case of surfaces in E fairly complete) theory, and in many cases to refer to the connections with the present stage ofdevelopment of the theory of multidimensional submanifolds. The leading question of the article is the problem of the connection between classes of metrics and classes of surfaces in En.
Mathematicians Of The World Unite
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Author : Guillermo Curbera
language : en
Publisher: CRC Press
Release Date : 2009-02-23
Mathematicians Of The World Unite written by Guillermo Curbera and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-23 with Mathematics categories.
This vividly illustrated history of the International Congress of Mathematicians- a meeting of mathematicians from around the world held roughly every four years- acts as a visual history of the 25 congresses held between 1897 and 2006, as well as a story of changes in the culture of mathematics over the past century. Because the congress is an int
Global Affine Differential Geometry Of Hypersurfaces
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Author : An-Min Li
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-08-17
Global Affine Differential Geometry Of Hypersurfaces written by An-Min Li and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-17 with Mathematics categories.
This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry – as differential geometry in general – has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces. The second edition of this monograph leads the reader from introductory concepts to recent research. Since the publication of the first edition in 1993 there appeared important new contributions, like the solutions of two different affine Bernstein conjectures, due to Chern and Calabi, respectively. Moreover, a large subclass of hyperbolic affine spheres were classified in recent years, namely the locally strongly convex Blaschke hypersurfaces that have parallel cubic form with respect to the Levi-Civita connection of the Blaschke metric. The authors of this book present such results and new methods of proof.
The Monge Amp Re Equation
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Author : Cristian E. Gutiérrez
language : en
Publisher: Birkhauser
Release Date : 2001
The Monge Amp Re Equation written by Cristian E. Gutiérrez and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Monge-Ampère equations categories.
The Monge-Amp re equation has attracted considerable interest in recent years because of its important role in several areas of applied mathematics. Monge-Amp re type equations have applications in the areas of differential geometry, the calculus of variations, and several optimization problems, such as the Monge-Kantorovitch mass transfer problem. This book stresses the geometric aspects of this beautiful theory, using techniques from harmonic analysis covering lemmas and set decompositions.