IAS/Park City Mathematics Series
Volume: 22;
2016;
456 pp;
Hardcover
MSC: Primary 53; 35; 83;
Print ISBN: 978-1-4704-2313-1
Product Code: PCMS/22
List Price: $99.00
AMS Member Price: $79.20
MAA Member Price: $89.10
Electronic ISBN: 978-1-4704-2881-5
Product Code: PCMS/22.E
List Price: $99.00
AMS Member Price: $79.20
MAA Member Price: $89.10
Geometric Analysis
Share this pageEdited by Hubert L. Bray; Greg Galloway; Rafe Mazzeo; Natasa Sesum
A co-publication of the AMS and IAS/Park City Mathematics Institute
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 Kähler-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.
Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.
Readership
Graduate students and research mathematicians interested in important topics in geometric analysis.
Reviews & Endorsements
It is a fascinating panorama of this highly active and deeply connected subject.
-- M. Kunzinger, Monatshefte für Mathematik
Table of Contents
Geometric Analysis
- Cover Cover11
- Title page iii4
- Contents v6
- Preface xiii14
- Introduction xv16
- Heat diffusion in geometry 118
- Applications of Hamilton’s compactness theorem for Ricci flow 1532
- The Kähler-Ricci flow on compact Kähler manifolds 5168
- Park City lectures on eigenfunctions 109126
- Critical metrics for Riemannian curvature functionals 195212
- Min-max theory and a proof of the Willmore conjecture 275292
- Weak immersions of surfaces with 𝐿²-bounded second fundamental form 301318
- Introduction to minimal surface theory 385402
- Back Cover Back Cover1457