Evolution for First Eigenvalue of LT,f on an Evolving Riemannian Manifold

In this paper, evolution formulas for the first non-zero eigenvalue of the operator LT,f on a weighted closed Riemannian manifold along the Ricci flow as well as along the Yamabe flow are formulated. Some monotonic quantities are also derived for the normalized Ricci flow on Bianchi classes.

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Bibliographic Details
Published inMathematics (Basel) Vol. 10; no. 23; p. 4614
Main Authors Saha, Apurba, Azami, Shahroud, Breaz, Daniel, Rapeanu, Eleonora, Hui, Shyamal Kumar
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2022
Subjects
eigenvalue
Eigenvalues
Evolution
Food science
homogeneous 3-manifold
Operators (mathematics)
Ricci flow
Riemann manifold
Yamabe flow
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Summary:In this paper, evolution formulas for the first non-zero eigenvalue of the operator LT,f on a weighted closed Riemannian manifold along the Ricci flow as well as along the Yamabe flow are formulated. Some monotonic quantities are also derived for the normalized Ricci flow on Bianchi classes.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10234614