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Received March 7, 2019; Accepted June 24, 2019; Published July 5, 2019
Abstract. Let (M,g) be an n-dimensional compact Riemannian manifold whose metric g(t) evolves by the generalised abstract geometric flow. This paper discusses the variation formulas, monotonicity and differentiability for the first eigenvalue of the p-Laplacian on (M,g(t)). It is shown that the first nonzero eigenvalue is monotonically nondecreasing along the flow under certain geometric conditions and that it is differentiable almost everywhere. These results provide a unified approach to the study of eigenvalue variations and applications under many geometric flows.
How to Cite this Article:
Abimbola Abolarinwa, Olukayode Adebimpe, Jing Mao, Variation of the first eigenvalue of p-Laplacian on evolving geometry and applications, Journal of Nonlinear Functional Analysis, Vol. 2019 (2019), Article ID 27, pp. 1-14.