Non-linear Elliptic Equations in Conformal Geometry
Sun-Yung Alice Chang(Author)
EMS Press
1st Edition
Published on 2. November 2004
Book
Paperback/Softback
VIII, 92 pages
978-3-03719-006-7 (ISBN)
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 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.
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.
More details
Series
Edition
1., Aufl.
Language
English
Place of publication
Zurich
Switzerland
Target group
College/higher education
Professional and scholarly
Students and researchers in mathematics seeking a quick introduction into the subject matter of the book.
Dimensions
Height: 24 cm
Width: 17 cm
Thickness: 6 mm
ISBN-13
978-3-03719-006-7 (9783037190067)
Schweitzer Classification