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# ðŸ“™ Non-linear elliptic equations in conformal geometry by Sun-yung Alice Chang â€” pdf free

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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.

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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**

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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 pl...

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 pl...

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 pl...

Product Description 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 r...

ORDINARY NON-LINEAR DIFFERENTIAL EQUATIONS IN ENGINEERING AND PHYSICAL SCIENCES BY N. W. McLACHLAN D. SC. ENGINEERING, LONDON OXFORD AT THE CLARENDON PRESS 1950 Oxford University Press, Amen House, London E. C, 4 GLASGOW NEW YORK TORONTO MELBOURNE WELLING...

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...

This book provides a self-contained development of the regularity theory for solutions of fully nonlinear elliptic equations. Caffarelli and CabrÃ© offer a detailed presentation of all techniques needed to extend the classical Schauder and CalderÃ³n-Zygmund...

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 ...

This book provides a self-contained development of the regularity theory for solutions of fully nonlinear elliptic equations. Caffarelli and CabrÃƒÂ© offer a detailed presentation of all techniques needed to extend the classical Schauder and CalderÃƒÂ³n-Zygmu...