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Full Description
This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kahler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in $R^3$, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace-Beltrami operators.
Contents
Heat diffusion in geometry by G. Huisken
Applications of Hamilton's compactness theorem for Ricci flow by P. Topping
The Kahler-Ricci flow on compact Kahler manifolds by B. Weinkove
Park City lectures on eigenfunctions by S. Zelditch
Critical metrics for Riemannian curvature functionals by J. A. Viaclovsky
Min-max theory and a proof of the Willmore conjecture by F. C. Marques and A. Neves
Weak immersions of surfaces with $L^2$-bounded second fundamental form by T. Riviere
Introduction to minimal surface theory by B. White
