Author : Y Matsushima
Publisher : World Scientific
Page : 788 pages
File Size : 41,82 MB
Release : 1992-04-15
Category : Mathematics
ISBN : 9814505919
In the past thirty years, differential geometry has undergone an enormous change with infusion of topology, Lie theory, complex analysis, algebraic geometry and partial differential equations. Professor Matsushima played a leading role in this transformation by bringing new techniques of Lie groups and Lie algebras into the study of real and complex manifolds. This volume is a collection of all the 46 papers written by him.
Author : Armand Borel
Publisher : Springer Science & Business Media
Page : 750 pages
File Size : 14,61 MB
Release : 1983
Category : Mathematics
ISBN : 9783540676409
This book collects the papers published by A. Borel from 1983 to 1999. About half of them are research papers, written on his own or in collaboration, on various topics pertaining mainly to algebraic or Lie groups, homogeneous spaces, arithmetic groups (L2-spectrum, automorphic forms, cohomology and covolumes), L2-cohomology of symmetric or locally symmetric spaces, and to the Oppenheim conjecture. Other publications include surveys and personal recollections (of D. Montgomery, Harish-Chandra, and A. Weil), considerations on mathematics in general and several articles of a historical nature: on the School of Mathematics at the Institute for Advanced Study, on N. Bourbaki and on selected aspects of the works of H. Weyl, C. Chevalley, E. Kolchin, J. Leray, and A. Weil. The book concludes with an essay on H. Poincaré and special relativity. Some comments on, and corrections to, a number of papers have also been added.
Author : Peter B Gilkey
Publisher : World Scientific
Page : 508 pages
File Size : 44,40 MB
Release : 2018-01-04
Category : Mathematics
ISBN : 9813220805
This volume focuses on discussing the interplay between the analysis, as exemplified by the eta invariant and other spectral invariants, the number theory, as exemplified by the relevant Dedekind sums and Rademacher reciprocity, the algebraic topology, as exemplified by the equivariant bordism groups, K-theory groups, and connective K-theory groups, and the geometry of spherical space forms, as exemplified by the Smith homomorphism. These are used to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group.This volume is a completely rewritten revision of the first edition. The underlying organization is modified to provide a better organized and more coherent treatment of the material involved. In addition, approximately 100 pages have been added to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. We have chosen to focus on the geometric aspect of the theory rather than more abstract algebraic constructions (like the assembly map) and to restrict our attention to spherical space forms rather than more general and more complicated geometrical examples to avoid losing contact with the fundamental geometry which is involved.
Author : Bang-yen Chen
Publisher : World Scientific Publishing Company
Page : 486 pages
File Size : 17,55 MB
Release : 2014-10-29
Category : Mathematics
ISBN : 9814616710
During the last four decades, there were numerous important developments on total mean curvature and the theory of finite type submanifolds. This unique and expanded second edition comprises a comprehensive account of the latest updates and new results that cover total mean curvature and submanifolds of finite type. The longstanding biharmonic conjecture of the author's and the generalized biharmonic conjectures are also presented in details. This book will be of use to graduate students and researchers in the field of geometry.
Author : Dan Branzei
Publisher : World Scientific
Page : 299 pages
File Size : 29,93 MB
Release : 1995-10-31
Category : Mathematics
ISBN : 9814500631
The book is an introduction to the foundations of Mathematics. The use of the constructive method in Arithmetic and the axiomatic method in Geometry gives a unitary understanding of the backgrounds of geometry, of its development and of its organic link with the study of real numbers and algebraic structures.
Author : Jian-Ke Lu
Publisher : World Scientific Publishing Company
Page : 312 pages
File Size : 37,80 MB
Release : 2002-11-26
Category : Mathematics
ISBN : 9813105992
This book is based on the teaching experience of the authors, and therefore some of the topics are presented in a new form. For instance, the multi-valued properties of the argument function are discussed in detail so that the beginner may readily grasp the elementary multi-valued analytic functions. The residue theorem is extended to the case where poles of analytic functions considered may occur on the boundary of a region — which is very useful in applications but not seen in textbooks written in English.
Author : De-lin Ren
Publisher : World Scientific Publishing Company
Page : 258 pages
File Size : 29,90 MB
Release : 1994-07-05
Category : Mathematics
ISBN : 9813103353
Essentials of integral geometry in a homogenous space are presented and the focus is on the basic results and applications. This book provides the readers with new findings, some being published for the first time and serves as an excellent graduate text.
Author : Roderick S C Wong
Publisher : World Scientific
Page : 557 pages
File Size : 50,43 MB
Release : 2000-06-30
Category : Mathematics
ISBN : 9814493066
This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.
Author : Jian-ke Lu
Publisher : World Scientific
Page : 482 pages
File Size : 14,89 MB
Release : 1994-02-04
Category : Mathematics
ISBN : 9814518026
This book deals with boundary value problems for analytic functions with applications to singular integral equations. New and simpler proofs of certain classical results such as the Plemelj formula, the Privalov theorem and the Poincaré-Bertrand formula are given. Nearly one third of this book contains the author's original works, most of which have not been published in English before and, hence, were previously unknown to most readers in the world.It consists of 7 chapters together with an appendix: Chapter I describes the basic knowledge on Cauchy-type integrals and Cauchy principal value integrals; Chapters II and III study, respectively, fundamental boundary value problems and their applications to singular integral equations for closed contours; Chapters IV and V discuss the same problems for curves with nodes (including open arcs); Chaper VI deals with similar problems for systems of functions; Chapter VII is concerned with some miscellaneous problems and the Appendix contains some basic results on Fredholm integral equations. In most sections, there are carefully selected sets of exercises, some of which supplement the text of the sections; answers/hints are also given for some of these exercises.For graduate students or seniors, all the 7 chapters can be used for a full year course, while the first 3 chapters may be used for a one-semester course.
Author : Goro Shimura
Publisher : Springer Science & Business Media
Page : 856 pages
File Size : 44,20 MB
Release : 2002-12-06
Category : Mathematics
ISBN : 9780387954165
In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement :" To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; concepts introduced by him were often seminal, and fertile ground for new developments, as witnessed by the many notations in number theory that carry his name and that have long been familiar to workers in the field." 103 of Shimura ́s most important papers are collected in four volumes. Volume II contains his mathematical papers from 1967 to 1977 and some notes to the articles.
