Ricci Solitons in Low Dimensions

AvBennett Chow

Häftad, Engelska, 2023

Del i serien Graduate Studies in Mathematics

1 064 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2023-11-30
Vikt:272 g
Format:Häftad
Språk:Engelska
Serie:Graduate Studies in Mathematics
Antal sidor:339
Förlag:American Mathematical Society
ISBN:9781470475239

Utforska kategorier

Topologi inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Mer om författaren

Bennett Chow, University of California, San Diego, La Jolla, CA.

Innehållsförteckning

Ricci flow singularity formationThe Ricci soliton equationThe $2$-dimensional classificationEstimates for shrinking Ricci solitonsClassification of $3$-dimensional shrinkersThe Bryant solitonExpanding and steady GRS and the flying wingBrendle's theorem on the uniqueness of $3$-dimensional steadiesGeometric preliminariesAnalytic preliminariesBibliographyIndex

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