Differential Harnack inequalities and the Ricci flow / Retro Müller.

Format:

Book

Author/Creator:

Müller, Reto, 1980-

Contributor:

Rosengarten Family Fund.

Series:

EMS series of lectures in mathematics

Language:

English

Subjects (All):

Ricci flow.

Differential inequalities.

Heat equation.

Global differential geometry.

Differential equations, Partial.

Physical Description:

vi, 92 pages ; 25 cm.

Place of Publication:

Zürich, Switzerland : European Mathematical Society, 2006.

Summary:

"The text is a self-contained, modern introduction to the Ricci flow and the analytic methods to study it. It is primarily addressed to students who have a basic introductory knowledge of analysis and of Riemannian geometry and who are attracted to further study in geometric analysis. No previous knowledge of differential Harnack inequalities or the Ricci flow is required."--BOOK JACKET.

Contents:

Foundational material: Riemannian metric and curvature tensors ; Variation formulas ; Einstein-Hilbert functional and Ricci flow ; Evolution equations under Ricci flow ; Adjoint heat equation and gradient solitons

Differential Harnack inequalities: The Li-Yau Harnack inequality ; Hamilton's matrix Harnack inequality ; Harnack inequalities for the Ricci flow

Entropy Formulas: The static case, part I ; Entropy for steady Ricci solitons ; The static case, part II ; Entropy for shrinking solitons ; Entropy for Ricci expanders

Reduced distance and reduced volume: The static case ; Perelman's L-length and L-geodesic ; Monotonicity of the reduced volume.

Notes:

Includes bibliographical references (pages 87-88) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

ISBN:

9783037190302

3037190302

OCLC:

76941925

Publisher Number:

9783037190302