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The Ricci flow was first introduced by R. Hamilton in the early 1980s, and is central in G. Perelman¿s celebrated proof of the Poincaré conjecture. When specialized for Kähler manifolds, it becomes the Kähler-Ricci flow, and reduces to a scalar PDE (parabolic complex Monge-Ampère equation).
As a spin-off of his breakthrough, G. Perelman proved the convergence of the Kähler-Ricci flow on Kähler-Einstein manifolds of positive scalar curvature (Fano manifolds). Shortly after, G. Tian and J. Song discovered a complex analogue of Perelman¿s ideas: the Kähler-Ricci flow is a metric embodiment of the Minimal Model Program of the underlying manifold, and flips and divisorial contractions assume the role of Perelman¿s surgeries.
The Ricci flow was first introduced by R. Hamilton in the early 1980s, and is central in G. Perelman¿s celebrated proof of the Poincaré conjecture. When specialized for Kähler manifolds, it becomes the Kähler-Ricci flow, and reduces to a scalar PDE (parabolic complex Monge-Ampère equation).
As a spin-off of his breakthrough, G. Perelman proved the convergence of the Kähler-Ricci flow on Kähler-Einstein manifolds of positive scalar curvature (Fano manifolds). Shortly after, G. Tian and J. Song discovered a complex analogue of Perelman¿s ideas: the Kähler-Ricci flow is a metric embodiment of the Minimal Model Program of the underlying manifold, and flips and divisorial contractions assume the role of Perelman¿s surgeries.
An educational and up-to-date reference work on non-linear parabolic partial differential equations
The only book currently available on the Kähler-Ricci flow
The first book to present a complete proof of Perelman's estimates for the Kähler-Ricci flow
Illustrates the connection between the Kähler-Ricci flow and the Minimal Model Program
Includes supplementary material: [...]
The (real) theory of fully non linear parabolic equations.- The KRF on positive Kodaira dimension Kähler manifolds.- The normalized Kähler-Ricci flow on Fano manifolds.- Bibliography.
| Erscheinungsjahr: | 2013 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 344 |
| Reihe: | Lecture Notes in Mathematics |
| Inhalt: |
viii
333 S. 10 s/w Illustr. 333 p. 10 illus. |
| ISBN-13: | 9783319008189 |
| ISBN-10: | 3319008188 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Redaktion: |
Boucksom, Sebastien
Guedj, Vincent Eyssidieux, Philippe |
| Herausgeber: | Sebastien Boucksom/Philippe Eyssidieux/Vincent Guedj |
| Auflage: | 2013 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Lecture Notes in Mathematics |
| Maße: | 235 x 155 x 19 mm |
| Von/Mit: | Sebastien Boucksom (u. a.) |
| Erscheinungsdatum: | 14.10.2013 |
| Gewicht: | 0,522 kg |
An educational and up-to-date reference work on non-linear parabolic partial differential equations
The only book currently available on the Kähler-Ricci flow
The first book to present a complete proof of Perelman's estimates for the Kähler-Ricci flow
Illustrates the connection between the Kähler-Ricci flow and the Minimal Model Program
Includes supplementary material: [...]
The (real) theory of fully non linear parabolic equations.- The KRF on positive Kodaira dimension Kähler manifolds.- The normalized Kähler-Ricci flow on Fano manifolds.- Bibliography.
| Erscheinungsjahr: | 2013 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 344 |
| Reihe: | Lecture Notes in Mathematics |
| Inhalt: |
viii
333 S. 10 s/w Illustr. 333 p. 10 illus. |
| ISBN-13: | 9783319008189 |
| ISBN-10: | 3319008188 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Redaktion: |
Boucksom, Sebastien
Guedj, Vincent Eyssidieux, Philippe |
| Herausgeber: | Sebastien Boucksom/Philippe Eyssidieux/Vincent Guedj |
| Auflage: | 2013 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Lecture Notes in Mathematics |
| Maße: | 235 x 155 x 19 mm |
| Von/Mit: | Sebastien Boucksom (u. a.) |
| Erscheinungsdatum: | 14.10.2013 |
| Gewicht: | 0,522 kg |
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