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Non-linear elliptic partial differential equations are an important tool in the study of Riemannian metrics in differential geometry, in particular for problems concerning the conformal change of metrics in Riemannian geometry. In recent years the role played by the second order semi-linear elliptic equations in the study of Gaussian curvature and scalar curvature has been extended to a family of fully non-linear elliptic equations associated with other symmetric functions of the Ricci tensor. A case of particular interest is the second symmetric function of the Ricci tensor in dimension four closely related to the Pfaffian. In these lectures, starting from the background material, the author reviews the problem of prescribing Gaussian curvature on compact surfaces. She then develops the analytic tools (e.g., higher order conformal invariant operators, Sobolev inequalities, blow-up analysis) in order to solve a fully nonlinear equation in prescribing the Chern-Gauss-Bonnet integrand on compact manifolds of dimension four. The material is suitable for graduate students and research mathematicians interested in geometry, topology, and differential equations. Distributed within the Americas by the American Mathematical Society.

## About book:

## About file:

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- Series:
**Zurich Lectures in Advanced Mathematics 1** - Author:
**Sun-yung Alice Chang** - Year:
**2004** - Publisher:
**EMS** - Language:
**English** - ISBN:
**303719006X,9783037190067**

- File size:
**1 092 876** - Format:
**pdf**

Security code:

This unique book explores the connections between the geometry of mappings and many important areas of modern mathematics such as Harmonic and non-linear Analysis, the theory of Partial Differential Equations, Conformal Geometry and Topology. Much of the...

Contents: MOTIVATION -- Non-linear elliptic equations in model problems; Linear algebraic systems; Linear elliptic problems; Non-linear algebraic systems and preconditioning. THEORETICAL BACKGROUND -- Non-linear equations in Hilbert space; Solvability of ...

The book is considered a systematic presentation of the modern quantum field theory of non-linear sigma-models. The content is based on original papers. Geometric properties and renormalization of a generic non-linear sigma-model are considered in detail,...

This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related line...

The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions.This book offers...

Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfac...

INTRODUCTION TO THE THEORY OF LINEAR DIFFERENTIAL EQUATIONS BY E. G. C. PODJLE Fellow of New College, Oxford OXFORD AT THE CLARENDON PRESS 193d Oui, 1 oeuvre sort plus belle Dune forme au travail Rebelle, Vers, marbre, onyx, email TH. GAUTIEB iZmaux et Ca...

Linear differential equations form the central topic of this volume, with the Galois theory being the unifying theme. A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithm...

Many mechanics and physics problems have variational formulations making them appropriate for numerical treatment by finite element techniques and efficient iterative methods. This book describes the mathematical background and reviews the techniques for ...

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Among the tests you perform on web applications, security testing is perhaps the most important, yet its often the most neglected. The recipes in the Web Security Testing Cookbook demonstrate how developers and testers can check for the most common web se...

Learn how individuals and couples can create wealth even if theyÐ²Ð‚â„¢re in debt. There are two areas to handling money effectively and creating wealth: One, the emotional area, and two, the practical area. Wealth On Any Income addresses both of these areas....

The 20 revised full papers presented in this book together with 4 section surveys were carefully reviewed and selected from the papers contributed to the 14th International Conference on Applications of Prolog, INAP 2001, held in Tokyo, Japan, in October ...

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This book provides a comprehensive text on Web data mining. Key topics of structure mining, content mining, and usage mining are covered. The book brings together all the essential concepts and algorithms from related areas such as data mining, machine le...

On the World Wide Web, people are accustomed to using graphical browsers such as Netscape Navigator or Mosaic as their only interface for visiting remote sites, accessing up-to-date documents, and filling out forms. But graphical browsers can be limiting...

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