Open AccessYamabe constant evolution and monotonicity along the conformal Ricci flow
Author(s) -
Yanlin Liu,
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.