Finsler Geometry and Applications (Ellis Horwood Series in Mathematics & Its Applications)
by Aurel Bejancu
Convex and Starlike Mappings in Several Complex Variables (Mathematics and Its Applications, #435)
by Sheng Gong
This interesting book deals with the theory of convex and starlike biholomorphic mappings in several complex variables. The underly- ing theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions. Because the author's introduction provides an excellent overview of the content of the book, I will not duplicate the effort here. Rather, I will place the book into historical context. The theory of univalent functions long has been an impor...
Variation et optimisation de formes (Mathematiques et Applications, v.48) (Mathimatiques Et Applications, #48)
by Antoine Henrot and Michel Pierre
Ce livre est une initiation aux approches modernes de l'optimisation mathematique de formes. Il s'appuie sur les seules connaissances de premiere annee de Master de mathematiques, mais permet deja d'aborder les questions ouvertes dans ce domaine en pleine effervescence. On y developpe la methodologie ainsi que les outils d'analyse mathematique et de geometrie necessaires a l'etude des variations de domaines. On y trouve une etude systematique des questions geometriques associees a l'operateur de...
Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications)
by Alexei Kushner, Valentin Lychagin, and Vladimir Rubtsov
Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a...
Manifolds, Sheaves, and Cohomology (Springer Studium Mathematik - Master)
by Torsten Wedhorn
This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.
'Guillemin and HaineaEURO (TM)s goal is to construct a well-documented road map that extends undergraduate understanding of multivariable calculus into the theory of differential forms. Throughout, the authors emphasize connections between differential forms and topology while making connections to single and multivariable calculus via the change of variables formula, vector space duals, physics; classical mechanisms, div, curl, grad, BrouweraEURO (TM)s fixed-point theorem, divergence theorem, a...
In the 25 years since their introduction, Higgs bundles have seen a surprising number of interactions within different areas of mathematics and physics. There is a recent surge of interest following Ngo Bau Chau's proof of the Fundamental Lemma and the work of Kapustin and Witten on the Geometric Langlands program. The program on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, was held at the Institute for Mathematical Sciences at the National University of Singapore during...
Celebrating the 50th Anniversary of the Journal of Differential Geometry (Surveys in Differential Geometry)
In 1967, C.-C. Hsiung at Lehigh University had the vision to form the Journal of Differential Geometry (JDG) - a journal dedicated to geometry alone. On the journal's fiftieth anniversary in 2017, a distinguished group of geometers gathered to present their papers at the annual JDG geometry and topology conference at Harvard University. This volume presents several of those papers, which include: Denis Auroux on speculations on homological mirror symmetry for hypersurfaces in Cn; Frances Kirwan...
Modern Differential Geometry in Gauge Theories Set (Progress in Mathematical Physics)
by Anastasios Mallios
Kahler Immersions of Kahler Manifolds into Complex Space Forms (Lecture Notes of the Unione Matematica Italiana, #23)
by Andrea Loi and Michela Zedda
The aim of this book is to describe Calabi's original work on Kahler immersions of Kahler manifolds into complex space forms, to provide a detailed account of what is known today on the subject and to point out some open problems. Calabi's pioneering work, making use of the powerful tool of the diastasis function, allowed him to obtain necessary and sufficient conditions for a neighbourhood of a point to be locally Kahler immersed into a finite or infinite-dimensional complex space form. This...
The aim of the Sino-Japan Conference of Young Mathematicians was to provide a forum for presenting and discussing recent trends and developments in differential equations and their applications, as well as to promote scientific exchanges and collaborations among young mathematicians both from China and Japan.The topics discussed in this proceedings include mean curvature flows, KAM theory, N-body problems, flows on Riemannian manifolds, hyperbolic systems, vortices, water waves, and reaction dif...
Differential Geometry in the Large (Lecture Notes in Mathematics, #1000)
by Heinz Hopf
These notes consist of two parts: Selected in York 1) Geometry, New 1946, Topics University Notes Peter Lax. by Differential in the 2) Lectures on Stanford Geometry Large, 1956, Notes J.W. University by Gray. are here with no essential They reproduced change. Heinz was a mathematician who mathema- Hopf recognized important tical ideas and new mathematical cases. In the phenomena through special the central idea the of a or difficulty problem simplest background is becomes clear. in this fashion...
Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem
by Stefan P Et Al Ivanov
Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space, the theory of minimal submanifolds have undergone considerable developments, involving techniques from related areas, such as the analysis of partial differential equations and complex analysis. On the other hand, the relativity theory has led to the study of pseudo-Riemannian manifolds, which turns out to be the most general framework for the study of minimal submani...
Structures On Manifolds (Series In Pure Mathematics, #3)
by Masahiro Kon and K Yano
Introduction to Geometry and Topology (Compact Textbooks in Mathematics)
by Werner Ballmann
This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of lecture courses. The first chapter covers elementary results and concepts from point-set topology. An exception is the Jordan Curve Theorem, which is proved for polygonal paths and is intended to give students a first glimpse into the nature of deeper topological problems. The second chapter of the book introduces manifolds and Lie grou...
During the academic year 1995/96, I was invited by the Scuola Normale Superiore to give a series of lectures. The purpose of these notes is to make the underlying economic problems and the mathematical theory of exterior differential systems accessible to a larger number of people. It is the purpose of these notes to go over these results at a more leisurely pace, keeping in mind that mathematicians are not familiar with economic theory and that very few people have read Elie Cartan.
World Market for Cereal Groats, Meal, and Pellets Excluding Those Made from Wheat, The: A 2007 Global Trade Perspective
by Philip M. Parker
Recent Advances in the Geometry of Submanifolds (Contemporary Mathematics)
This volume contains the proceedings of the AMS Special Session on Geometry of Submanifolds, held from October 25-26, 2014, at San Francisco State University, San Francisco, CA, and the AMS Special Session on Recent Advances in the Geometry of Submanifolds: Dedicated to the Memory of Franki Dillen (1963-2013), held from March 14-15, 2015, at Michigan State University, East Lansing, Ml. The focus of the volume is on recent studies of submanifolds of Riemannian, semi-Riemannian, Kaehlerian and con...
Direct and Inverse Methods in Nonlinear Evolution Equations (Lecture Notes in Physics, #632)
by Robert M. Conte, Franco Magri, Micheline Musette, Junkichi Satsuma, and Pavel Winternitz
Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities a la Painleve, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main...
Differentialgeometrie Von Kurven Und Flachen (Vieweg Studium; Aufbaukurs Mathematik)
by Manfredo P Carmo
Es gibt in der Differentialgeometrie von Kurven und FJachen zwei Betrachtungsweisen. Die eine, die man klassische Differentialgeometrie nennen konnte, entstand zusammen mit den Anfangen der Differential-und Integralrechnung. Grob gesagt studiert die klassische Differentialgeometrie lokale Eigenschaften von Kurven und FHichen. Dabei verstehen wir unter lokalen Eigenschaften solche, die nur vom Verhalten der Kurve oder Flache in der Umgebung eines Punktes abhiingen. Die Methoden, die sich als fUr...
Noncommutative Geometry and Optimal Transport (Contemporary Mathematics)
This volume contains the proceedings of the Workshop on Noncommutative Geometry and Optimal Transport, held on November 27, 2014, in Besancon, France. The distance formula in noncommutative geometry was introduced by Connes at the end of the 1980s. It is a generalization of Riemannian geodesic distance that makes sense in a noncommutative setting, and provides an original tool to study the geometry of the space of states on an algebra. It also has an intriguing echo in physics, for it yields a...