Extrinsic geometric flows

著者

書誌事項

Extrinsic geometric flows

Ben Andrews, Bennett Chow, Christine Guenther, Mat Langford

（Graduate studies in mathematics, 206）

American Mathematical Society, 2021

  • : softcover

大学図書館所蔵 件 / 全2件

この図書・雑誌をさがす

注記

"c2020 by the authors. All rights reserved. "--T.p. verso

"Reprinted by the American Mathematical Society, 2021"--T.p. verso

Includes bibliographical references (p. 727-752) and index

内容説明・目次

内容説明

Extrinsic geometric flows are characterized by a submanifold evolving in an ambient space with velocity determined by its extrinsic curvature. The goal of this book is to give an extensive introduction to a few of the most prominent extrinsic flows, namely, the curve shortening flow, the mean curvature flow, the Gauss curvature flow, the inverse-mean curvature flow, and fully nonlinear flows of mean curvature and inverse-mean curvature type. The authors highlight techniques and behaviors that frequently arise in the study of these (and other) flows. To illustrate the broad applicability of the techniques developed, they also consider general classes of fully nonlinear curvature flows. The book is written at the level of a graduate student who has had a basic course in differential geometry and has some familiarity with partial differential equations. It is intended also to be useful as a reference for specialists. In general, the authors provide detailed proofs, although for some more specialized results they may only present the main ideas; in such cases, they provide references for complete proofs. A brief survey of additional topics, with extensive references, can be found in the notes and commentary at the end of each chapter.

目次

The heat equation Introduction to curve shortening The Gage-Hamilton-Grayson theorem Self-similar and ancient solutions Hypersurfaces in Euclidean space Introduction to mean curvature flow Mean curvature flow of entire graphs Huisken's theorem Mean convex mean curvature flow Monotonicity formulae Singularity analysis Noncollapsing Self-similar solutions Ancient solutions Gauss curvature flows The affine normal flow Flows by superaffine powers of the Gauss curvature Fully nonlinear curvature flows Flows of mean curvature type Flows of inverse-mean curvature type Bibliography Index

「Nielsen BookData」 より

関連文献： 1件中  1-1を表示

詳細情報

ページトップへ