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may 2020 A class of monotonic quantities along the Yamabe flow
Farzad Daneshvar, Asadollah Razavi
Bull. Belg. Math. Soc. Simon Stevin 27(1): 17-27 (may 2020). DOI: 10.36045/bbms/1590199300

Abstract

Let $(M,g(t))$ be a closed Riemannian manifold of dimension $n\geq 2$. In this paper we obtain the evolution formula for the lowest constant $\lambda^{b}_{a}(g)$ under the normalized and unnormalized Yamabe flow such that the equation \begin{equation*} -{\rm \Delta} f + af\log f + bRf= \lambda^{b}_{a}(g) f, \end{equation*} with $\int_M f^2\, {\rm dV}=1,$ has positive solutions, where $a$ and $b$ are two real constants. Then we construct various monotonic quantities under the normalized and unnormalized Yamabe flow. We also show that the scalar curvature of a steady Yamabe breather with nonnegative scalar curvature is identically zero.

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Farzad Daneshvar. Asadollah Razavi. "A class of monotonic quantities along the Yamabe flow." Bull. Belg. Math. Soc. Simon Stevin 27 (1) 17 - 27, may 2020. https://doi.org/10.36045/bbms/1590199300

Information

Published: may 2020
First available in Project Euclid: 23 May 2020

zbMATH: 07213654
MathSciNet: MR4102697
Digital Object Identifier: 10.36045/bbms/1590199300

Subjects:
Primary: 53C21, 53C44

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 1 • may 2020
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