On the spectrum of the weighted p-Laplacian under the Ricci-harmonic flow
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Springer
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This paper studies the behaviour of the spectrum of the weighted p-Laplacian on a
complete Riemannian manifold evolving by the Ricci-harmonic flow. Precisely, the
first eigenvalue diverges in a finite time along this flow. It is further shown that the
same divergence result holds on gradient shrinking and steady almost Ricci-harmonic
solitons under the condition that the soliton function is nonnegative and
superharmonic. We also continue the program in (Abolarinwa, Adebimpe and Bakare
in J. Ineq. Appl. 2019:10, 2019) to the case of volume-preserving Ricci-harmonic flow.
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QA Mathematics