Ricci solitons in low dimensions / Bennett Chow.

Format:

Book

Author/Creator:

Chow, Bennett, author.

Series:

Graduate studies in mathematics ; v.235.

Graduate studies in mathematics, 1065-7339 ; volume 235

Language:

English

Subjects (All):

Global differential geometry.

Ricci flow.

Solitons.

Riemannian manifolds.

Physical Description:

xvi, 339 pages : illustrations ; 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2023]

Summary:

"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."-- Back cover.

Contents:

Ricci flow singularity formation

The Ricci soliton equation

The 2-dimensional classification

Estimates for shrinking Ricci solutions

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.

Notes:

Includes bibliographical references and index.

ISBN:

9781470474287

147047428X

9781470475239

1470475235

OCLC:

1393206019