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SpringerBriefs in Mathematics

Brakke's Mean Curvature Flow

An Introduction

Authors: Tonegawa, Yoshihiro

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  • Is the first exposition of Brakke’s mean curvature flow, a subject that interests many researchers
  • Uses accessible language, not highly technical terminology, for all readers interested in geometric measure theory
  • Explains recent highly acclaimed research results of the mean curvature flow
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イーブック ¥5,615
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-981-13-7075-5
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ソフトカバー ¥7,019
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-981-13-7074-8
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
  • Usually dispatched within 3 to 5 business days.
この書籍について

This book explains the notion of Brakke’s mean curvature flow and its existence and regularity theories without assuming familiarity with geometric measure theory. The focus of study is a time-parameterized family of k-dimensional surfaces in the n-dimensional Euclidean space (1 ≤ n). The family is the mean curvature flow if the velocity of motion of surfaces is given by the mean curvature at each point and time. It is one of the simplest and most important geometric evolution problems with a strong connection to minimal surface theory. In fact, equilibrium of mean curvature flow corresponds precisely to minimal surface. Brakke’s mean curvature flow was first introduced in 1978 as a mathematical model describing the motion of grain boundaries in an annealing pure metal. The grain boundaries move by the mean curvature flow while retaining singularities such as triple junction points. By using a notion of generalized surface called a varifold from geometric measure theory which allows the presence of singularities, Brakke successfully gave it a definition and presented its existence and regularity theories. Recently, the author provided a complete proof of Brakke’s existence and regularity theorems, which form the content of the latter half of the book. The regularity theorem is also a natural generalization of Allard’s regularity theorem, which is a fundamental regularity result for minimal surfaces and for surfaces with bounded mean curvature. By carefully presenting a minimal amount of mathematical tools, often only with intuitive explanation, this book serves as a good starting point for the study of this fascinating object as well as a comprehensive introduction to other important notions from geometric measure theory.

Table of contents (6 chapters)

Table of contents (6 chapters)

書籍の購入

イーブック ¥5,615
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-981-13-7075-5
  • ウォーターマーク付、 DRMフリー
  • ファイル形式: EPUB, PDF
  • どの電子書籍リーダーからでもすぐにお読みいただけます。
  • ご購入後、すぐにダウンロードしていただけます。
ソフトカバー ¥7,019
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-981-13-7074-8
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
  • Usually dispatched within 3 to 5 business days.
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書誌情報

Bibliographic Information
Book Title
Brakke's Mean Curvature Flow
Book Subtitle
An Introduction
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2019
Publisher
Springer Singapore
Copyright Holder
The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
イーブック ISBN
978-981-13-7075-5
DOI
10.1007/978-981-13-7075-5
ソフトカバー ISBN
978-981-13-7074-8
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XII, 100
Number of Illustrations
12 b/w illustrations
Topics