Differential Harnack Inequalities and the Ricci Flow (Record no. 50363)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03473nam a22004335a 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783037195307 |
| 100 1# - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Müller, Reto, |
| 245 10 - TITLE STATEMENT | |
| Title | Differential Harnack Inequalities and the Ricci Flow |
| Statement of responsibility, etc | Reto Müller |
| 260 3# - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Zuerich, Switzerland : |
| Name of publisher | European Mathematical Society Publishing House, |
| Year of publication | 2006 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 1 online resource (99 pages) |
| 490 0# - SERIES STATEMENT | |
| Series statement | EMS Series of Lectures in Mathematics (ELM) |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | The classical Harnack inequalities play an important role in the study of parabolic partial differential equations. The idea of finding a differential version of such a classical Harnack inequality goes back to Peter Li and Shing Tung Yau, who introduced a pointwise gradient estimate for a solution of the linear heat equation on a manifold which leads to a classical Harnack type inequality if being integrated along a path. Their idea has been successfully adopted and generalized to (nonlinear) geometric heat flows such as mean curvature flow or Ricci flow; most of this work was done by Richard Hamilton. 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. This approach forms the main analytic core of Perelman's attempt to prove the Poincaré conjecture. It is, however, of completely independent interest and may as well prove useful in various other areas, such as, for instance, the theory of Kähler manifolds. 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 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. |
| 650 07 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Differential & Riemannian geometry |
| 650 07 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Differential equations |
| 650 07 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Global analysis, analysis on manifolds |
| 650 07 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Partial differential equations |
| 650 07 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Differential geometry |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Müller, Reto, |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://doi.org/10.4171/030 |
| 856 42 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://www.ems-ph.org/img/books/mueller_mini.jpg |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | E-BOOKS |
| 264 #1 - | |
| -- | Zuerich, Switzerland : |
| -- | European Mathematical Society Publishing House, |
| -- | 2006 |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Accession Number | Uniform Resource Identifier | Koha item type |
|---|---|---|---|---|---|---|---|
| IMSc Library | EBK13739 | https://doi.org/10.4171/030 | E-BOOKS |