Riemannian Geometry and Geometric Analysis (Paperback)
暫譯: 黎曼幾何與幾何分析（平裝本）

Jost, Jürgen

Riemannian Geometry and Geometric Analysis (Paperback)
  • 出版商: Springer
  • 出版日期: 2017-10-23
  • 售價: $3,600
  • 貴賓價: 9.5 折 $3,420
  • 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)

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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)

這本已建立的參考書繼續為讀者提供通往當代幾何學中一些最有趣發展的入口。它深入探討了廣泛的主題，包括黎曼幾何的基本概念，如測地線、聯結和曲率；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；以及理論物理中最重要的變分原則，如Yang-Mills、Ginzburg-Landau或量子場論的非線性σ模型。本卷將所有這些主題連接在一個系統的幾何框架中。同時，它為讀者提供了該領域的工作工具，使其能夠深入進行幾何研究。

第七版已系統性地重新組織和更新。幾乎沒有頁面未經修改。它還包括新材料，例如關於辛幾何的內容，以及Bishop-Gromov體積增長定理，該定理闡明了Ricci曲率的幾何角色。

來自評論：「這本書提供了對黎曼幾何和幾何分析的非常易讀的介紹……隨著幾何分析這一數學主題的廣泛發展，這本教科書非常受歡迎。」數學評論

「對於熟悉微分幾何基礎和對現代分析有一定了解的讀者來說，這本書是相對自足的。這本書在奠定現代黎曼幾何和幾何分析的基礎方面做得非常好。它介紹了多個關鍵技術，並提供了該領域的代表性概述。」數學月刊

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)

尤爾根·約斯特是德國萊比錫馬克斯·普朗克科學數學研究所的共同所長，萊比錫大學數學與計算機科學系的名譽教授，以及美國新墨西哥州聖塔菲複雜科學研究所的外部教員。

他是多本施普林格（Springer）教科書的作者，包括《後現代分析》（Postmodern Analysis，1997、2002、2005）、《緊湊的黎曼曲面》（Compact Riemann Surfaces，1997、2002、2006）、《偏微分方程》（Partial Differential Equations，2002、2007、2013）、《微分幾何與最小表面》（Differentialgeometrie und Minimalflächen，1994、2007、2014，與 J. Eschenburg 合著）、《動力系統》（Dynamical Systems，2005）、《數學概念》（Mathematical Concepts，2015），以及幾本研究專著，如《幾何與物理》（Geometry and Physics，2009），並在科學期刊上發表了許多論文。

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