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Ricci Solitons in Low Dimensions
 
Bennett Chow University of California, San Diego, La Jolla, CA
Hardcover ISBN:  978-1-4704-7428-7
Product Code:  GSM/235
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Softcover ISBN:  978-1-4704-7523-9
Product Code:  GSM/235.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7522-2
Product Code:  GSM/235.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-7428-7
eBook: ISBN:  978-1-4704-7522-2
Product Code:  GSM/235.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
Softcover ISBN:  978-1-4704-7523-9
eBook: ISBN:  978-1-4704-7522-2
Product Code:  GSM/235.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
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Ricci Solitons in Low Dimensions
Bennett Chow University of California, San Diego, La Jolla, CA
Hardcover ISBN:  978-1-4704-7428-7
Product Code:  GSM/235
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Softcover ISBN:  978-1-4704-7523-9
Product Code:  GSM/235.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7522-2
Product Code:  GSM/235.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-7428-7
eBook ISBN:  978-1-4704-7522-2
Product Code:  GSM/235.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
Softcover ISBN:  978-1-4704-7523-9
eBook ISBN:  978-1-4704-7522-2
Product Code:  GSM/235.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 2352023; 339 pp
    MSC: Primary 53; 58; 57; 30

    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 manifold's 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.

    Readership

    Graduate students and researchers interested in Ricci flow and Ricci solitons.

  • Table of Contents
     
     
    • Chapters
    • Ricci flow singularity formation
    • The Ricci soliton equation
    • The $2$-dimensional classification
    • Estimates for shrinking Ricci solitons
    • Classification of $3$-dimensional shrinkers
    • The Bryant soliton
    • Expanding and steady GRS and the flying wing
    • Brendle’s theorem on the uniqueness of $3$-dimensional steadies
    • Geometric preliminaries
    • Analytic preliminaries
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 2352023; 339 pp
MSC: Primary 53; 58; 57; 30

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 manifold's 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.

Readership

Graduate students and researchers interested in Ricci flow and Ricci solitons.

  • Chapters
  • Ricci flow singularity formation
  • The Ricci soliton equation
  • The $2$-dimensional classification
  • Estimates for shrinking Ricci solitons
  • Classification of $3$-dimensional shrinkers
  • The Bryant soliton
  • Expanding and steady GRS and the flying wing
  • Brendle’s theorem on the uniqueness of $3$-dimensional steadies
  • Geometric preliminaries
  • Analytic preliminaries
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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