On the spectrum of the weighted p -Laplacian under the Ricci-harmonic flow

[摘要] 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.

[学科分类] 电力

[关键词] Ricci harmonic flow;Laplace–Beltrami operator;Eigenvalue;Monotonicity;Ricci solitons