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Non-linear Elliptic Equations in Con...

Chang, Sun-Yung Alice,

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Non-linear Elliptic Equations in Conformal Geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Non-linear Elliptic Equations in Conformal Geometry/ Sun-Yung Alice Chang
Author:	Chang, Sun-Yung Alice,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2004,
Description:	1 online resource (100 pages)
Subject:	Differential & Riemannian geometry -
Online resource:	https://doi.org/10.4171/006
Online resource:	https://www.ems-ph.org/img/books/chang_mini.jpg
ISBN:	9783037195062

Non-linear Elliptic Equations in Conformal Geometry
Chang, Sun-Yung Alice,

Non-linear Elliptic Equations in Conformal Geometry[electronic resource] /Sun-Yung Alice Chang - Zuerich, Switzerland :European Mathematical Society Publishing House,2004 - 1 online resource (100 pages) - Zurich Lectures in Advanced Mathematics (ZLAM).

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

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.

ISBN: 9783037195062

Standard No.: 10.4171/006doiSubjects--Topical Terms:

3480810
Differential & Riemannian geometry

Non-linear Elliptic Equations in Conformal Geometry
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520 $a 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.
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