Differential Harnack inequalities and the Ricci flow / Retro Müller.

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Bibliographic Details
Uniform Title:EMS series of lectures in mathematics.
Main Author: Müller, Reto, 1964-
Language:English
Published: Zürich, Switzerland : European Mathematical Society, 2006.
Series:EMS series of lectures in mathematics.
Subjects:
Global differential geometry.
Ricci flow.
Differential equations, Partial.
Physical Description:vi, 92 pages ; 25 cm.
Format: Book
Contents:
  • Preface
  • Introduction
  • 1. 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
  • 2. DIFFERENTIAL HARNACK INEQUALITIES. The Li-Yau Harnack inequality
  • Hamilton's matrix Harnack inequality
  • Harnack inequalities for the Ricci flow
  • 3. 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
  • 4. REDUCED DISTANCE AND REDUCED VOLUME. The static case
  • Perelman's L-length and L-geodesic
  • Monotonicity of the reduced volume
  • Bibliography
  • List of symbols
  • Index.