Description
The Workshop on Geometric Evolution Equations was a gathering of
experts that produced this comprehensive collection of articles.
Many of the papers relate to the Ricci flow and Hamilton's
program for understanding the geometry and topology of 3-manifolds.
The use of evolution equations in geometry can lead to remarkable
results. Of particular interest is the potential solution of
Thurston's Geometrization Conjecture and the Poincare Conjecture.
Yet applying the method poses serious technical problems.
Contributors to this volume explain some of these issues and
demonstrate a noteworthy deftness in the handling of technical
areas.
Various topics in geometric evolution equations and related
fields are presented. Among other topics covered are minimal
surface equations, mean curvature flow, harmonic map flow, Calabi
flow, Ricci flow (including a numerical study), Kahler-Ricci
flow, function theory on Kahler manifolds, flows of plane curves,
convexity estimates, and the Christoffel-Minkowski problem.
The material is suitable for graduate students and researchers
interested in geometric analysis and connections to topology.
Related titles of interest include The Ricci Flow: An
Introduction.
Contents
S. Angenent and J. Hulshof -- Singularities at t=infty in
equivariant harmonic map flow
S.-C. Chang -- Recent developments on the Calabi flow
A. Chau -- Stability of the Kahler-Ricci flow at complete non-compact
Kahler Einstein metrics
B. Chow -- A survey of Hamilton's program for the Ricci flow on 3-manifolds
S.-C. Chu -- Basic properties of gradient Ricci solitons
D. Garfinkle and J. Isenberg -- Numerical studies of the behavior
of Ricci flow
P. Guan and X.-N. Ma -- Convex solutions of fully nonlinear
elliptic equations in classical differential geometry
R. Gulliver -- Density estimates for minimal surfaces and
surfaces flowing by mean curvature
D. Knopf -- An introduction to the Ricci flow neckpinch
L. Ni -- Monotonicity and Kahler-Ricci flow
M. Simon -- Deforming Lipschitz metrics into smooth metrics while
keeping their curvature operator non-negative
L.-F. Tam -- Liouville properties on Kahler manifolds
D.-H. Tsai -- Expanding embedded plane curves
M.-T. Wang -- Remarks on a class of solutions to the minimal
surface system
Details:
Series: Contemporary Mathematics, Volume: 367
Publication Year: 2005
ISBN: 0-8218-3361-8
Paging: 235 pp.
Binding: Softcover
Expected publication date is March 9, 2005
Description
This volume is dedicated to Francois Treves, who made substantial
contributions to the geometric side of the theory of partial
differential equations (PDEs) and several complex variables. One
of his best-known contributions, reflected in many of the
articles here, is the study of hypo-analytic structures.
An international group of well-known mathematicians has
contributed to the volume. Articles generally reflect the
interaction of geometry and analysis that is typical of Treves's
work, such as the study of the special types of partial
differential equations that arise in conjunction with CR-manifolds,
symplectic geometry, or special families of vector fields. There
are many topics in analysis and PDEs covered here, unified by
their connections to geometry.
The material is suitable for graduate students and research
mathematicians interested in geometric analysis of PDEs and
several complex variables.
Contents
P. Ahern and X. Gong -- Cusp-type singularities of real analytic
curves in the complex plane
S. Berhanu and J. Hounie -- The F. and M. Riesz property for
vector fields
A. Bove -- Gevrey hypo-ellipticity for sums of squares of vector
fields: Some examples
H. Brezis, P. Mironescu, and A. C. Ponce -- W^{1,1}-maps with
values into S^1
S. Chanillo -- Analytic hypoellipticity and spectral problems for
Schrodinger's equation
H. Chen and Z. Luo -- Formal solutions for higher order nonlinear
totally characteristic PDEs with irregular singularities
F. Colombini and N. Lerner -- Uniqueness of L^infty solutions for
a class of conormal BV vector fields
P. D. Cordaro and N. Hanges -- Impact of lower order terms on a
model pde in two variables
M. Derridj and D. S. Tartakoff -- Global analytic hypoellipticity
for a class of quasilinear sums of squares of vector fields
M. Eastwood -- Representations via overdetermined systems
G. Francsics and P. D. Lax -- A semi-explicit fundamental domain
for a Picard modular group in complex hyperbolic space
S. Gindikin -- Complex horospherical transform on real sphere
J. Gorsky and A. A. Himonas -- On analyticity in space variable
of solutions to the KdV equation
L. Hormander -- The multinomial distribution and some Bergman
kernels
X. Huang, S. Ji, and D. Xu -- Several results for holomorphic
mappings from B^n into B^N
H. Jacobowitz -- Whitney and Mizohata structures
A. E. Kogoj and E. Lanconelli -- One-side Liouville theorems for
a class of hypoelliptic ultraparabolic equations
L. Lempert -- Acyclic sheaves in Banach spaces
A. Li and Y. Y. Li -- A Liouville type theorem for some
conformally invariant fully nonlinear equations
S. T. Melo -- Norm closure of classical pseudodifferential
operators does not contain Hormander's class
G. Metivier -- Remarks on the well-posedness of the nonlinear
Cauchy problem
A. Meziani -- Representation of solutions of planar elliptic
vector fields with degeneracies
L. Nirenberg -- Some recollections of working with Francois
Treves
M.-C. Shaw -- Boundary value problems on Lipschitz domains in
mathbb{R}^n or mathbb{C}^n
S. Spagnolo -- Hyperbolic systems well posed in all Gevrey
classes
Details:
Series: Contemporary Mathematics, Volume: 368
Publication Year: 2005
ISBN: 0-8218-3386-3
Paging: 414 pp.
Binding: Softcover
Expected publication date is March 16, 2005
Description
A Special Session on affine and algebraic geometry was held at
the first joint meeting between the American Mathematical Society
(AMS) and the Real Sociedad Matematica Espanola (RSME) held in
Seville (Spain). This volume contains articles by participating
speakers at the Session.
The book contains research and survey papers discussing recent
progress on the Jacobian Conjecture and affine algebraic geometry
and includes a large collection of open problems. It is suitable
for graduate students and research mathematicians interested in
algebraic geometry.
Contents
Open problems in affine algebraic geometry (collected by G.
Freudenburg and P. Russell)
T. Asanuma -- Purely inseparable k-forms of affine algebraic
curves
T. Asanuma, S. M. Bhatwadekar, and N. Onoda -- Generic fibrations
by A^1 and A^* over discrete valuation rings
M. de Bondt and A. van den Essen -- Hesse and the Jacobian
Conjecture
P. Cassou-Nogues -- Bad field generators
V. Drensky -- Coordinates in ideals of polynomial algebras
H. Flenner and M. Zaidenberg -- On the uniqueness of mathbb{C}^*-actions
on affine surfaces
T. Kambayashi and M. Miyanishi -- On two recent views of the
Jacobian Conjecture
T. Kishimoto -- Singularities on normal affine 3-folds containing
mathbb{A}^1-cylinderlike open subsets
H. Kraft -- Free mathbb{C}^+-actions on affine threefolds
L. Makar-Limanov -- Again x+x^2y+z^2+t^3=0
K. Masuda and M. Miyanishi -- Equivariant cancellation for
algebraic varieties
R. Peretz -- Constructing polynomial mappings using non-commutative
algebras
T. Shaska and J. L. Thompson -- On the generic curve of genus 3
I. E. Shparlinski -- Orders of points on elliptic curves
V. Shpilrain and J.-T. Yu -- Test polynomials, retracts, and the
Jacobian conjecture
D. Wright -- The Jacobian Conjecture: ideal membership questions
and recent advances
Details:
Series: Contemporary Mathematics,Volume: 369
Publication Year: 2005
ISBN: 0-8218-3476-2
Paging: 276 pp.
Binding: Softcover
Expected publication date is March 31, 2005
Description
Comprised of papers from the IIIrd Prairie Analysis Seminar held
at Kansas State University, this book reflects the many
directions of current research in harmonic analysis and partial
differential equations. Included is the work of the distinguished
main speaker, Tadeusz Iwaniec, his invited guests John Lewis and
Juan Manfredi, and many other leading researchers.
The main topic is the so-called p-harmonic equation, which is a
family of nonlinear partial differential equations generalizing
the usual Laplace equation. This study of p-harmonic equations
touches upon many areas of analysis with deep relations to
functional analysis, potential theory, and calculus of variations.
The material is suitable for graduate students and research
mathematicians interested in harmonic analysis and partial
differential equations.
Contents
F. H. Beatrous, T. J. Bieske, and J. J. Manfredi -- The maximum
principle for vector fields
I. Blank -- A partial classification of the blowups of the
singularities in a composite membrane problem
A. Domokos and J. J. Manfredi -- C^{1,alpha}-regularity for p-harmonic
functions in the Heisenberg group for p near 2
L. D'Onofrio and T. Iwaniec -- Notes on p-harmonic analysis
M. Foss -- A condition sufficient for the partial regularity of
minimizers in two-dimensional nonlinear elasticity
C. Frosini -- Dynamics on bounded domains
K. E. Hare and A. M. Stokolos -- On the rate of tangential
convergence of functions from Hardy spaces, 0<p<1
P. A. Hasto -- Counter-examples of regularity in variable
exponent Sobolev spaces
L. V. Kovalev and D. Opela -- Quasiregular gradient mappings and
strong solutions of elliptic equations
R. S. Krausshar, Y. Qiao, and J. Ryan -- Harmonic, monogenic and
hypermonogenic functions on some conformally flat manifolds in
R^n arising from special arithmetic groups of the Vahlen group
J. L. Lewis -- On symmetry and uniform rectifiability arising
from some overdetermined elliptic and parabolic boundary
conditions
L. Forzani and D. Maldonado -- Recent progress on the Monge-Ampere
equation
J. Onninen -- Mappings of finite distortion: Future directions
and problems
M. Stawiska -- Riemann-Hurwitz formula and Morse theory
Details:
Series: Contemporary Mathematics, Volume: 370
Publication Year: 2005
ISBN: 0-8218-3610-2
Paging: 211 pp.
Binding: Softcover
Expected publication date is April 7, 2005
Description
The Stony Brook Conference, "Graphs and Patterns in
Mathematics and Theoretical Physics", was dedicated to
Dennis Sullivan in honor of his sixtieth birthday. The event's
scientific content, which was suggested by Sullivan, was largely
based on mini-courses and survey lectures. The main idea was to
help researchers and graduate students in mathematics and
theoretical physics who encounter graphs in their research to
overcome conceptual barriers.
The collection begins with Sullivan's paper, "Sigma models
and string topology," which describes a background algebraic
structure for the sigma model based on algebraic topology and
transversality. Other contributions to the volume were organized
into five sections: Feynman Diagrams, Algebraic Structures,
Manifolds: Invariants and Mirror Symmetry, Combinatorial Aspects
of Dynamics, and Physics. These sections, along with more
research-oriented articles, contain the following surveys: "Feynman
diagrams for pedestrians and mathematicians" by M. Polyak,
"Notes on universal algebra" by A. Voronov, "Unimodal
maps and hierarchical models" by M. Yampolsky, and "Quantum
geometry in action: big bang and black holes" by A. Ashtekar.
This comprehensive volume is suitable for graduate students and
research mathematicians interested in graph theory and its
applications in mathematics and physics.
Contents
D. Sullivan -- Sigma models and string topology
Feynman diagrams
M. Polyak -- Feynman diagrams for pedestrians and mathematicians
D. Kreimer -- Structures in Feynman graphs: Hopf algebras and
symmetries
Algebraic structures
A. A. Voronov -- Notes on universal algebra
D. Tamarkin and B. Tsygan -- The ring of differential operators
on forms in noncommutative calculus
V. Gorbounov, F. Malikov, and V. Schechtman -- Twisted chiral de
Rham algebras on mathbb{P}^1
Manifolds: Invariants and mirror symmetry
R. Kashaev and N. Reshetikhin -- Invariants of tangles with flat
connections in their complements
S. Garoufalidis and J. Levine -- Tree-level invariants of three-manifolds,
Massey products and the Johnson homomorphism
K. Fukaya -- Multivalued Morse theory, asymptotic analysis and
mirror symmetry
Combinatorial aspects of dynamics
R. Forman -- Some applications of combinatorial differential
topology
A. de Carvalho -- Extensions, quotients and generalized pseudo-Anosov
maps
M. Yampolsky -- Unimodal maps and hierarchical models
Physics
A. Ashtekar -- Quantum geometry in action: big bang and black
holes
P. van Nieuwenhuizen -- Supersymmetry, supergravity, superspace
and BRST symmetry in a simple model
Details:
Series: Proceedings of Symposia in Pure Mathematics, Volume: 73
Publication Year: 2005
ISBN: 0-8218-3666-8
Paging: 418 pp.
Binding: Hardcover