Non-linear elliptic equations in conformal geometry

Non-linear elliptic equations in conformal geometry

by Chang, Sun-Yung A.

Type Book
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"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."--BOOK JACKET.

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Title Statements

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

Summary

"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."--BOOK JACKET.

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Edition Statements

  • Publication Date:©2004.

Publication Statements

The Physical Object

  • Description:viii, 92 pages ; : 24 cm.

Edition Identifiers

  • ISBN:303719006X, 9783037190067
  • oclc:ocm58414868
  • LC Classification:QA377
  • Dewey Decimal:515.3533

Table of Contents

1. Gaussian curvature equation -- 2. Moser-Trudinger inequality (on the sphere) -- 3. Polyakov formula on compact surfaces -- 4. Conformal covariant operators -- Paneitz operator -- 5. Functional determinant on 4-manifolds -- 6. Extremal metrics for the log-determinant functional -- 7. Elementary symmetric functions -- 8. A priori estimates for the regularized equation (*)[delta] -- 9. Smoothing via the Yamabe flow -- 10. Deforming [sigma][subscript 2] to a constant function

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Subjects

Conformal geometry Curvature Differential equations, Elliptic Differential equations, Nonlinear Differentialgeometrie Elliptic operators Équations différentielles elliptiques Équations différentielles non linéaires Konforme Differentialgeometrie Opérateurs elliptiques Topological manifolds Variétés topologiques

Writers

Chang, Sun-Yung A.

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