Riemannian Geometry and Geometric Analysis (Paperback)

Jost, Jürgen

  • 出版商: Springer
  • 出版日期: 2017-10-23
  • 售價: $3,930
  • 貴賓價: 9.5$3,734
  • 語言: 英文
  • 頁數: 697
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3319618598
  • ISBN-13: 9783319618593
  • 相關分類: 物理學 Physics
  • 立即出貨 (庫存=1)

買這商品的人也買了...

商品描述

This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research.
The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature.

From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome." Mathematical Reviews

"For readers familiar with the basics of differential geometry and some acquaintance with modern analysis, the book is reasonably self-contained. The book succeeds very well in laying out the foundations of modern Riemannian geometry and geometric analysis. It introduces a number of key techniques and provides a representative overview of the field." Monatshefte f r Mathematik



 

商品描述(中文翻譯)

這本權威的參考書持續為讀者提供了一個通往當代幾何學中最有趣發展的入口。它提供了對各種主題的深入洞察,包括黎曼幾何的基本概念,如測地線、連接和曲率;幾何分析的基本模型和工具,如調和函數、形式、映射、特徵值、Dirac算子和熱流方法;以及理論物理學中最重要的變分原理,如楊-米爾斯、金茲堡-蘭道或量子場論的非線性西格瑪模型。本書以系統的幾何框架將所有這些主題聯繫在一起。同時,它為讀者提供了這個領域的工作工具,使他們能夠深入研究幾何學。

第七版已經進行了系統的重新組織和更新。幾乎每一頁都有所改變。它還包括新的材料,例如輪廓幾何,以及闡明了黎曼曲率在幾何學中的幾何角色的Bishop-Gromov體積增長定理。

「從評論中可以看出:」這本書提供了一個非常易讀的黎曼幾何和幾何分析入門...隨著幾何分析這一數學學科的巨大發展,這本教科書非常受歡迎。」《數學評論》

「對於熟悉微分幾何基礎並對現代分析有一定了解的讀者來說,這本書是相當自成一體的。這本書在奠定現代黎曼幾何和幾何分析基礎方面非常成功。它介紹了一些關鍵技術,並提供了該領域的代表性概述。」《數學月報》

作者簡介

Jürgen Jost is Codirector of the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, an Honorary Professor at the Department of Mathematics and Computer Sciences at Leipzig University, and an External Faculty Member of the Santa Fe Institute for the Sciences of Complexity, New Mexico, USA.

 

He is the author of a number of further Springer textbooks including Postmodern Analysis (1997, 2002, 2005), Compact Riemann Surfaces (1997, 2002, 2006), Partial Differential Equations (2002, 2007, 2013), Differentialgeometrie und Minimalflächen (1994, 2007, 2014, with J. Eschenburg), Dynamical Systems (2005), Mathematical Concepts (2015), as well as several research monographs, such as Geometry and Physics (2009), and many publications in scientific journals.

 

 

 

 

作者簡介(中文翻譯)

Jürgen Jost是德國萊比錫萊比錫大學數學與計算機科學系的名譽教授,也是德國萊比錫科學數學研究所的聯合主任,以及美國新墨西哥州聖塔菲科學複雜性研究所的外部教職成員。

他是Springer出版社的多本教科書的作者,包括《後現代分析》(1997年,2002年,2005年)、《緊致黎曼曲面》(1997年,2002年,2006年)、《偏微分方程》(2002年,2007年,2013年)、《微分幾何與極小曲面》(1994年,2007年,2014年,與J. Eschenburg合著)、《動力系統》(2005年)、《數學概念》(2015年),以及多本研究專著,如《幾何與物理學》(2009年),以及許多科學期刊上的發表。