<p>Based on lectures held at the Center for Theoretical Sciences in Taiwan in honor of Louis Nirenberg’s 75th birthday, the volume contains both research papers dealing with various problems in Partial Differential Equations such as wave maps, the Navier-Stokes equations, and Lagrangian submanifolds. </p>
<p>Professor Nirenberg is particularly appreciated for his generous encouragement of the development of mathematics in the Asia-Pacific region and the mixture of articles by distinguished mathematicians from Asia and other parts of the world.</p>

Lectures on Partial Differential Equations: Proceedings in honor of Louis Nirenberg's 75th Birthday

Science & Math

Horng-Tzer Yau

Sun-Yung Alice Chang

Chang-Shou Lin

Mathematics

International Press of Boston

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.

Non-Linear Elliptic Equations in Conformal Geometry (Zurich Lectures in Advanced Mathematics)

European Mathematical Society

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