Yamabe constant evolution and monotonicity along the conformal Ricci flow | Zendy

Yanlin Li | Zendy; Abimbola Abolarinwa | Zendy; Shahroud Azami | Zendy; Akram Ali | Zendy

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Yamabe constant evolution and monotonicity along the conformal Ricci flow

Author(s) -

Yanlin Li,

Abimbola Abolarinwa,

Shahroud Azami,

Akram Ali

Publication year - 2022

Publication title -

aims mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.329

H-Index - 15

ISSN - 2473-6988

DOI - 10.3934/math.2022671

Subject(s) - yamabe flow , ricci flow , conformal map , constant (computer programming) , mathematics , metric (unit) , monotonic function , flow (mathematics) , ricci curvature , mathematical physics , physics , mathematical analysis , scalar curvature , geometry , computer science , operations management , curvature , sectional curvature , economics , programming language

We investigate the Yamabe constant's behaviour in a conformal Ricci flow. For conformal Ricci flow metric $ g(t) $, $ t \in [0, T) $, the time evolution formula for the Yamabe constant $ Y(g(t)) $ is derived. It is demonstrated that if the beginning metric $ g(0) = g_0 $ is Yamabe metric, then the Yamabe constant is monotonically growing along the conformal Ricci flow under some simple assumptions unless $ g_0 $ is Einstein. As a result, this study adds to the body of knowledge about the Yamabe problem.

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