New from International Press, July 2008
Surveys in Differential Geometry
Volume 12
Geometric Flows
Edited by
Huai-Dong Cao (Lehigh University)
Shing-Tung Yau (Harvard University)
This twelfth volume of the annual Surveys in Differential Geometry examines recent developments on a number of geometric flows and related subjects, such as Hamilton’s Ricci flow, formation of singularities in the mean curvature flow, the Kähler-Ricci flow, and Yau’s uniformization conjecture.
Publication details
Hardcover. 356 pages.
ISBN-13: 978-1-57146-118-6
ISBN-10: 1-57146-118-3
2000 MSC: 53C44
Newly published: July 2008
Publisher: International Press of Boston
List price $85. Discounts may apply.
Full description
Geometric flows are non-linear parabolic differential equations which describe the evolution of geometric structures. Inspired by Hamilton’s Ricci flow, the field of geometric flows has seen tremendous progress in the past 25 years and yields important applications to geometry, topology, physics, nonlinear analysis, and so on. Of course, the most spectacular development is Hamilton’s theory of Ricci flow and its application to three-manifold topology, including the Hamilton-Perelman proof of the Poincaré conjecture.
This twelfth volume of the annual Surveys in Differential Geometry examines recent developments on a number of geometric flows and related subjects, such as Hamilton’s Ricci flow, formation of singularities in the mean curvature flow, the Kähler-Ricci flow, and Yau’s uniformization conjecture.
Table of Contents
- On the conformal scalar curvature equation and related problems
(S. Brendle) - A survey of the Kähler-Ricci Flow and Yau’s Uniformization Conjecture
(A. Chau, L.-F. Tam) - Recent developments on the Hamilton’s Ricci Flow
(H.-D. Cao, B.-L. Chen, and X.-P. Zhu) - Curvature flows in semi-Riemannian manifolds
(C. Gerhardt) - Global regularity and singularity development for wave maps
(J. Krieger) - Relativistic Teichmüller theory: a Hamilton-Jacobi approach to 2+1-dimensional Einstein gravity
(V. Moncrief) - Monotonicity and Li-Yau-Hamilton inequalities
(L. Ni) - Singularities of mean curvature flow and flow with surgeries
(C. Sinestrari) - Some recent developments in Lagrangian mean curvature flows
(M.-T. Wang)
About the series
The editors of the highly esteemed Journal of Differential Geometry (published by International Press) each year present a new volume of Surveys in Differential Geometry, a collection of original contributions upon a specially chosen topic pertaining to differential geometry and related topics. The series presents an overview of recent trends, while making predictions and suggestions for future research.
Each invited contributor is a prominent specialist in the field of algebraic geometry, mathematical physics, or related areas. Contributors to Surveys tend to transcend classical frameworks within their field.
Once every three years, Lehigh University and Harvard University, in conjunction with the editors of the JDG, sponsor a conference whose purpose is to survey the general field of differential geometry and related subjects. Speakers at the conference are likewise selected for their prominence in a given field and for their innovative contributions to it. Hence every third volume of Surveys is a publication of those presented talks.
The Surveys in Differential Geometry series is a beneficial collection for experts and non-experts alike, and in particular, for those independent of the mainstream of activity in the field of geometry.
Recent volumes of the Surveys in Differential Geometry series
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