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Müller R. — Differential harnack inequalities and the ricci flow
Müller R. — Differential harnack inequalities and the ricci flow

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Название: Differential harnack inequalities and the ricci flow

Автор: Müller R.


In 2002, Grisha Perelman presented a new kind of differential Harnack inequality which involves both the (adjoint) linear heat equation and the Ricci flow. This led to a completely new approach to the Ricci flow that allowed interpretation as a gradient flow which maximizes different entropy functionals. The goal of this book is to explain this analytic tool in full detail for the two examples of the linear heat equation and the Ricci flow. It begins with the original Li-Yau result, presents Hamilton's Harnack inequalities for the Ricci flow, and ends with Perelman's entropy formulas and space-time geodesics. The book 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. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 92

Добавлена в каталог: 16.10.2012

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Предметный указатель
$\mathcal{L}$-exponential map      76
$\mathcal{L}$-geodesic      69 74
Adjoint heat operator      23
Backwards reduced distance      65 75
Backwards reduced volume      65 84
Bianchi identities      13
Christoffel symbols      11
Cigar soliton      5
Connection      11
Convex boundary      31
Cut locus      76
Dirichlet functional      47
Divergence operator      14
Einstein summation      11
Einstein tensor      17
Einstein — Hilbert functional      17
Elliptic operator      28
entropy      65
Entropy for steadies      49
Entropy, gradient      26
Entropy, heat equation      53
Evolution of connection      21
Evolution of curvature      19
Evolution of dV      21
Evolution of Laplacian      21
Evolution of Ricci tensor      19
Evolution of Riemann tensor      19
expanders      24
Exponential map      12
Extended      11
Forward reduced volume      66
Geodesic      68
Hamack inequality for heat kernel      58
Hamack inequality for Ricci flow      43 45
Hamack inequality, Hamilton’s matrix      37
Hamack inequality, Li — Yau      31
Hamack inequality, Perelman’s      64
Hamilton’s matrix Hamack      37
Heat operator      22
Heat operator, adjoint      23
Heat operator, injectivity domain      76
Integrated version      42
Levi — Civita connection      11
Li — Yau Hamack      31
Li — Yau Hamack, integrated version      34
Li — Yau Hamack, quadratic version      32
Lichnerowicz Laplacian      14
Lie-brackets      21
Lie-derivative      24
Maximum principle      29
Maximum principle for matrices      37
Maximum principle for systems      35
Nash entropy      47
Nash entropy, modified      57
Ni’s entropy      53
Ni’s entropy local version      54
Normal coordinates      12
Parabolic boundary      28
Parabolic cylinder      28
Parabolic interior      28
Parabolic operator      28
Perelman’s $\mathfrak{F}$-entropy      49
Perelman’s $\mathfrak{W}$-entropy      62
Perelman’s $\mathfrak{W}$-entropy, local version      62
Perelman’s Hamack      64
Quadratic version      40
Reduced distance      59
Reduced volume      72
Ricci curvature      12
Ricci flow      17
Ricci flow, backwards      22
Ricci flow, Hamack inequality      43 45
Ricci solitons      24
Riemannian curvature      12
Riemannian metric      11
Scalar curvature      12
Second fundamental form      31
Shrinkers      24
Shrinkers, entropy      62
Shrinkers, gradient      25
Soliton      24
Soliton, cigar      5
Soliton, gradient expander      26
Soliton, gradient shrinker      25
Soliton, gradient steady      24
Space-time, connection      45
Space-time, manifold      45
Space-time, path      46
Stationary metric      17
Steadies      24
Steadies, entropy      49
Steadies, gradient      24
Support function      35
Support function of curvature      15
Support function of dV      16
Support function of Ricci tensor      15
Support function of Riemann tensor      15
Support function, variation      14
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