First Eigenvalues of Some Operators Under the Backward Ricci Flow on Bianchi Classes

Autor:	Shahroud Azami, Rawan Bossly, Abdul Haseeb, Abimbola Abolarinwa
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	Ricci flow p-Laplacian operator eigenvalue Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 23, p 3846 (2024)
Druh dokumentu:	article
ISSN:	12233846 2227-7390
DOI:	10.3390/math12233846
Popis:	Let λ(t) be the first eigenvalue of the operator −∆+aRb on locally three-dimensional homogeneous manifolds along the backward Ricci flow, where a,b are real constants and R is the scalar curvature. In this paper, we study the properties of λ(t) on Bianchi classes. We begin by deriving an evolution equation for the quantity λ(t) on three-dimensional homogeneous manifolds in the context of the backward Ricci flow. Utilizing this equation, we subsequently establish a monotonic quantity that is contingent upon λ(t). Additionally, we present both upper and lower bounds for λ(t) within the framework of Bianchi classes.
Databáze:	Directory of Open Access Journals
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