Non-linear elliptic equations in conformal geometry

by Chang, Sun-Yung A.

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Title Statements

Full title :Non-linear elliptic equations in conformal geometry / Sun-Yung Alice Chang.

Summary

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.

Edition Statements

Publication Date:©2004

Publication Statements

Publisher(s):European Mathematical Society
Place of Publication:Zürich, Switzerland
Language:eng
Publication Date:©2004

The Physical Object

Description:1 online resource (viii, 92 pages).

Edition Identifiers

ISBN:3037195061, 9783037195062
DOI:10.4171/006
oclc:ocn656239046
LC Classification:QA377
Dewey Decimal:515.353

Subjects

Differential & Riemannian geometry Differential equations Differential equations, Elliptic Differential equations, Nonlinear DIFFERENTIAL GEOMETRY Electronic books Elliptic operators Équations différentielles elliptiques Équations différentielles non linéaires Global analysis, analysis on manifolds Manifolds and cell complexes Opérateurs elliptiques Partial Differential Equations Topological manifolds Variétés topologiques