The Ricci Flow: An Introduction

Chow, Bennett; Knopf, Dan

ISBN 10: 0821835157 / ISBN 13: 9780821835159

Verlag: American Mathematical Society, Providence, RI, 2004

Beschreibung

Hard cover, no jacket intended, from the collection of a London Professor of Mathematics, (ret'd.). In fine condition, pages tightly bound, content unmarked. CN.

Bestandsnummer des Verkäufers 616310

Bibliografische Details

• Titel: The Ricci Flow: An Introduction
• Verlag: American Mathematical Society, Providence, RI
• Erscheinungsjahr: 2004
• Sprache: Englisch
• ISBN-10: 0821835157
• ISBN-13: 9780821835159
• Einband: Hardcover
• Zustand: Very Good
• Zustand des Schutzumschlags: No Dust Jacket
• Verkäuferkataloge:
  • Mathematics/Accounting

Über diesen Titel

Inhaltsangabe

The Ricci flow is a powerful technique that integrates geometry, topology, and analysis. Intuitively, the idea is to set up a PDE that evolves a metric according to its Ricci curvature. The resulting equation has much in common with the heat equation, which tends to 'flow' a given function to ever nicer functions. By analogy, the Ricci flow evolves an initial metric into improved metrics. Richard Hamilton began the systematic use of the Ricci flow in the early 1980s and applied it in particular to study 3-manifolds. Grisha Perelman has made recent breakthroughs aimed at completing Hamilton's program. The Ricci flow method is now central to our understanding of the geometry and topology of manifolds.This book is an introduction to that program and to its connection to Thurston's geometrization conjecture. The authors also provide a 'Guide for the hurried reader', to help readers wishing to develop, as efficiently as possible, a nontechnical appreciation of the Ricci flow program for 3-manifolds, i.e., the so-called 'fast track'. The book is suitable for geometers and others who are interested in the use of geometric analysis to study the structure of manifolds. ""The Ricci Flow"" was nominated for the 2005 Robert W. Hamilton Book Award, which is the highest honor of literary achievement given to published authors at the University of Texas at Austin.

Reseña del editor

The Ricci flow is a powerful technique that integrates geometry, topology, and analysis. Intuitively, the idea is to set up a PDE that evolves a metric according to its Ricci curvature. The resulting equation has much in common with the heat equation, which tends to ``flow'' a given function to ever nicer functions. By analogy, the Ricci flow evolves an initial metric into improved metrics. Richard Hamilton began the systematic use of the Ricci flow in the early 1980s and applied it in particular to study 3-manifolds. Grisha Perelman has made recent breakthroughs aimed at completing Hamilton's program. The Ricci flow method is now central to our understanding of the geometry and topology of manifolds. This book is an introduction to that program and to its connection to Thurston's geometrization conjecture. The authors also provide a ``Guide for the hurried reader'', to help readers wishing to develop, as efficiently as possible, a nontechnical appreciation of the Ricci flow program for 3-manifolds, i.e., the so-called ``fast track''. The book is suitable for geometers and others who are interested in the use of geometric analysis to study the structure of manifolds.