Ricci solitons in low dimensions:
Preliminary review / Publishers description: Ricci flow is an exciting subject of mathematics with diverse applications in geometry, topology, and other fields. It employs a heat-type equation to smooth an initial Riemannian metric on a manifold. The formation of singularities in the manifolds topol...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2023]
|
| Schriftenreihe: | Graduate studies in mathematics
Volume 235 |
| Schlagworte: |
Global analysis, analysis on manifolds
> Partial differential equations on manifolds; differential operators
> Elliptic equations on manifolds, general theory
Global analysis, analysis on manifolds
> Partial differential equations on manifolds; differential operators
> Heat and other parabolic equation methods
Global analysis, analysis on manifolds
> Partial differential equations on manifolds; differential operators
> Relations with special manifold structures (Riemannian, Finsler, etc.)
|
| Online-Zugang: | Volltext |
| Zusammenfassung: | Preliminary review / Publishers description: Ricci flow is an exciting subject of mathematics with diverse applications in geometry, topology, and other fields. It employs a heat-type equation to smooth an initial Riemannian metric on a manifold. The formation of singularities in the manifolds topology and geometry is a desirable outcome. Upon closer examination, these singularities often reveal intriguing structures known as Ricci solitons. This introductory book focuses on Ricci solitons, shedding light on their role in understanding singularity formation in Ricci flow and formulating surgery-based Ricci flow, which holds potential applications in topology. Notably successful in dimension 3, the book narrows its scope to low dimensions: 2 and 3, where the theory of Ricci solitons is well established. A comprehensive discussion of this theory is provided, while also establishing the groundwork for exploring Ricci solitons in higher dimensions. A particularly exciting area of study involves the potential applications of Ricci flow in comprehending the topology of 4-dimensional smooth manifolds. Geared towards graduate students who have completed a one-semester course on Riemannian geometry, this book serves as an ideal resource for related courses or seminars centered on Ricci solitons. |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | 1 Online-Ressource (xvi, 339 Seiten) Illustrationen, Diagramme |
| ISBN: | 9781470475222 9781470474287 |
| DOI: | 10.1090/gsm/235 |
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| 490 | 1 | |a Graduate studies in mathematics |v Volume 235 | |
| 500 | |a Includes bibliographical references and index | ||
| 520 | |a Preliminary review / Publishers description: Ricci flow is an exciting subject of mathematics with diverse applications in geometry, topology, and other fields. It employs a heat-type equation to smooth an initial Riemannian metric on a manifold. The formation of singularities in the manifolds topology and geometry is a desirable outcome. Upon closer examination, these singularities often reveal intriguing structures known as Ricci solitons. This introductory book focuses on Ricci solitons, shedding light on their role in understanding singularity formation in Ricci flow and formulating surgery-based Ricci flow, which holds potential applications in topology. Notably successful in dimension 3, the book narrows its scope to low dimensions: 2 and 3, where the theory of Ricci solitons is well established. A comprehensive discussion of this theory is provided, while also establishing the groundwork for exploring Ricci solitons in higher dimensions. A particularly exciting area of study involves the potential applications of Ricci flow in comprehending the topology of 4-dimensional smooth manifolds. Geared towards graduate students who have completed a one-semester course on Riemannian geometry, this book serves as an ideal resource for related courses or seminars centered on Ricci solitons. | ||
| 650 | 7 | |a Global differential geometry |2 DLC | |
| 650 | 7 | |a Ricci flow |2 DLC | |
| 650 | 7 | |a Solitons |2 DLC | |
| 650 | 7 | |a Riemannian manifolds |2 DLC | |
| 653 | 0 | |a Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Elliptic equations on manifolds, general theory | |
| 653 | 0 | |a Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Heat and other parabolic equation methods | |
| 653 | 0 | |a Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Relations with special manifold structures (Riemannian, Finsler, etc.) | |
| 653 | 0 | |a Manifolds and cell complexes -- Low-dimensional topology -- Geometric structures on low-dimensional manifolds | |
| 653 | 0 | |a Functions of a complex variable -- Riemann surfaces -- Classification theory of Riemann surfaces | |
| 653 | 0 | |a Functions of a complex variable -- Riemann surfaces -- Conformal metrics (hyperbolic, Poincaré, distance functions) | |
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| id | DE-604.BV050061357 |
| illustrated | Illustrated |
| indexdate | 2025-01-28T11:08:58Z |
| institution | BVB |
| isbn | 9781470475222 9781470474287 |
| language | English |
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| physical | 1 Online-Ressource (xvi, 339 Seiten) Illustrationen, Diagramme |
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| spelling | Chow, Bennett 1962- (DE-588)136099793 aut Ricci solitons in low dimensions Bennett Chow Providence, Rhode Island American Mathematical Society [2023] © 2023 1 Online-Ressource (xvi, 339 Seiten) Illustrationen, Diagramme txt rdacontent c rdamedia cr rdacarrier Graduate studies in mathematics Volume 235 Includes bibliographical references and index Preliminary review / Publishers description: Ricci flow is an exciting subject of mathematics with diverse applications in geometry, topology, and other fields. It employs a heat-type equation to smooth an initial Riemannian metric on a manifold. The formation of singularities in the manifolds topology and geometry is a desirable outcome. Upon closer examination, these singularities often reveal intriguing structures known as Ricci solitons. This introductory book focuses on Ricci solitons, shedding light on their role in understanding singularity formation in Ricci flow and formulating surgery-based Ricci flow, which holds potential applications in topology. Notably successful in dimension 3, the book narrows its scope to low dimensions: 2 and 3, where the theory of Ricci solitons is well established. A comprehensive discussion of this theory is provided, while also establishing the groundwork for exploring Ricci solitons in higher dimensions. A particularly exciting area of study involves the potential applications of Ricci flow in comprehending the topology of 4-dimensional smooth manifolds. Geared towards graduate students who have completed a one-semester course on Riemannian geometry, this book serves as an ideal resource for related courses or seminars centered on Ricci solitons. Global differential geometry DLC Ricci flow DLC Solitons DLC Riemannian manifolds DLC Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Elliptic equations on manifolds, general theory Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Heat and other parabolic equation methods Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Relations with special manifold structures (Riemannian, Finsler, etc.) Manifolds and cell complexes -- Low-dimensional topology -- Geometric structures on low-dimensional manifolds Functions of a complex variable -- Riemann surfaces -- Classification theory of Riemann surfaces Functions of a complex variable -- Riemann surfaces -- Conformal metrics (hyperbolic, Poincaré, distance functions) Erscheint auch als Druck-Ausgabe 978-1-4704-7428-7 Graduate studies in mathematics Volume 235 (DE-604)BV044714883 235 https://doi.org/10.1090/gsm/235 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Chow, Bennett 1962- Ricci solitons in low dimensions Graduate studies in mathematics Global differential geometry DLC Ricci flow DLC Solitons DLC Riemannian manifolds DLC |
| title | Ricci solitons in low dimensions |
| title_auth | Ricci solitons in low dimensions |
| title_exact_search | Ricci solitons in low dimensions |
| title_full | Ricci solitons in low dimensions Bennett Chow |
| title_fullStr | Ricci solitons in low dimensions Bennett Chow |
| title_full_unstemmed | Ricci solitons in low dimensions Bennett Chow |
| title_short | Ricci solitons in low dimensions |
| title_sort | ricci solitons in low dimensions |
| topic | Global differential geometry DLC Ricci flow DLC Solitons DLC Riemannian manifolds DLC |
| topic_facet | Global differential geometry Ricci flow Solitons Riemannian manifolds |
| url | https://doi.org/10.1090/gsm/235 |
| volume_link | (DE-604)BV044714883 |
| work_keys_str_mv | AT chowbennett riccisolitonsinlowdimensions |