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 Kahler-Ricci flow, and Yau’s uniformization conjecture.
Publication details
Hardcover. 356 pages.
ISBN-13: 978-1-57146-118-6
July 2008
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
Poincare 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 Kahler-Ricci flow, and Yau’s uniformization conjecture.
* On the conformal scalar curvature equation and related problems
(S. Brendle)
* A survey of the Kahler-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 Teichmuller 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)
This much-anticipated revised second edition of Christopher Sogge’s 1995
work provides a self-contained account of the basic facts concerning the
linear wave equation and the methods from harmonic analysis that are
necessary when studying nonlinear hyperbolic differential equations.
Publication details
Hardcover. 203 pages.
ISBN-13: 978-1-57146-173-5
July 2008
This much-anticipated revised second edition of Christopher Sogge’s 1995
work provides a self-contained account of the basic facts concerning the
linear wave equation and the methods from harmonic analysis that are
necessary when studying nonlinear hyperbolic differential equations. Sogge
examines quasilinear equations with small data where the Klainerman-Sobolev
inequalities and weighted space-time estimates are introduced to prove
global existence results. New simplified arguments are given in the current
edition that allow one to handle quasilinear systems with multiple wave
speeds. The next topic concerns semilinear equations with small initial
data. John’s existence theorem for R1+3 is discussed with blow-up problems
and some results for the spherically symmetric case. After this, general
Strichartz estimates are treated. A proof of the endpoint Strichartz
estimates of Keel and Tao and the Christ-Kiselev lemma are given, the
material being new in this edition. Using the Strichartz estimates, the
critical wave equation in R1+3 is studied.
* Chapter 1: Background and groundwork
* Linear wave equation: a review
* Energy inequality: a first version
* Existence and uniqueness for linear equations
* Local existence for quasilinear equations
* Local existence for semilinear equations in (1 + 3)-dimensions
* Notes
* Chapter 2: Quasilinear equations with small data
* Klainerman-Sobolev inequalities
* Global existence in higher dimensions
* A weighted energy estimate
* Almost global existence for symmetric systems
* Null condition and global existence when n=3
* The restriction theorem and local existence revisited
* Notes
* Chapter 3: Semilinear equations with small data
* Strichartz’s estimate for the wave equation
* John’s existence theorem for R1+3
* Blow-up for small powers
* Notes
* Chapter 4: General Strichartz estimates
* The endpoint Strichartz estimates of Keel and Tao
* The Christ-Kiselev lemma and inhomogeneous estimates
* An application: Existence theorems for rough data
* Improved results under spherical symmetry
* Notes
* Chapter 5: Global existence for semilinear equations with large data
* Main results
* Energy estimates and the subcritical case
* A decay lemma and the critical case
* Notes
* Appendix: Some tools from classical analysis
ISBN-13: 978-0-19-955644-1
Estimated publication date: November 2008
304 pages, 234x156 mm
First comprehensive treatment of this topic.
Clear exposition.
Thorough coverage of background material.
Good selection of applications.
Includes basic molecular theory and concentration dependence.
Brownian motion - the incessant motion of small particles suspended in a fluid - is an important topic in statistical physics and physical chemistry. This book studies its origin in molecular scale fluctuations, its description in terms of random process theory and also in terms of statistical mechanics. A number of new applications of these descriptions to physical and chemical processes, as well as statistical mechanical derivations and the mathematical background are discussed in detail. Graduate students, lecturers, and researchers in statistical physics and physical chemistry will find this an interesting and useful reference work.
Readership: Graduate students, lecturers, and researchers in statistical physics and physical chemistry.
1. Historical background
2. Probability theory
3. Stochastic processes
4. Einstein-Smoluchowski Theory
5. Stochastic differential equations and integrals
6. Functional integrals
7. Some important special cases
8. The Smoluchowski Equation
9. Random walk
10. Statistical mechanics
11. Stochastic equations from a statistical mechanical viewpoint
12. Two exactly treatable models
13. Brownian Motion and noise
14. Diffusion phenomena
15. Rotational diffusion
16. Polymer solutions
17. Interacting Brownian Particles
18. Dynamics, fractals, and chaos
A. The applicability of Stokes Law
B. Functional calculus
C. An operator identity
D. Euler Angles
E. The Oseen Tensor
F. Mutual- and self-diffusion
The art of origami, or paper folding, is carried out using a square piece of paper to obtain attractive figures of animals, flowers or other familiar figures. It is easy to see that origami has links with geometry. Creases and edges represent lines, intersecting creases and edges make angles, while the intersections themselves represent points. Because of its manipulative and experiential nature, origami could become an effective context for the learning and teaching of geometry.
In this unique and original book, origami is an object of mathematical exploration. The activities in this book differ from ordinary origami in that no figures of objects result. Rather, they lead the reader to study the effects of the folding and seek patterns. The experimental approach that characterizes much of science activity can be recognized throughout the book, as the manipulative nature of origami allows much experimenting, comparing, visualizing, discovering and conjecturing.
The reader is encouraged to fill in all the proofs, for his/her own satisfaction and for the sake of mathematical completeness. Thus, this book provides a useful, alternative approach for reinforcing and applying the theorems of high school mathematics.
A Point Opens the Door to Origamics
New Folds Bring Out New Theorems
Extension of the Haga’s Theorems to Silver Ratio Rectangles
X-Lines with Lots of Surprises
“Intrasquares” and “Extrasquares”
A Petal Pattern from Hexagons?
Heptagon Regions Exist?
A Wonder of Eleven Stars
Where to Go and Whom to Meet
Inspiration of Rectangular Paper
150pp (approx.) Pub. date: Scheduled Winter 2008
ISBN 978-981-283-489-8
ISBN 978-981-283-490-4(pbk)
The Fourth Conference on Infinite Dimensional Harmonic Analysis brought together experts in harmonic analysis, operator algebras and probability theory. Most of the articles deal with the limit behavior of systems with many degrees of freedom in the presence of symmetry constraints. This volume gives new directions in research bringing together stochastic analysis and representation theory.
Mathematical Analysis of Some Geometric Illusions (H Arai)
Transforms, Polynomials and Integrable Models Associated with Reflection Groups (C F Dunkl)
A Variant of the Frobenius Reciprocity for Restricted Representations on Nilpotent Lie Groups (H Fujiwara et al.)
Positive and Negative Definite Functions on Hypergroups and Their Duals (H Heyer)
Projective Representations and Spin Characters of Finite and Infinite Complex Reflection Groups (T Hirai et al.)
Semibounded Unitary Representations of Infinite Dimensional Lie Groups (K-H Neeb)
Limit Theorems for Radial Random Walks of High Dimensions (M Voit)
and other papers
Readership: Researchers in analysis and differential equations, geometry and topology, probability and statistics.
350pp (approx.) Pub. date: Scheduled Fall 2008
ISBN 978-981-283-281-8