Evolution and monotonicity of the first eigenvalue of p-Laplacian under the Ricci-harmonic flow

• Autorzy: Abolarinwa A.

Identyfikatory

DOI

10.1515/jaa-2015-0013

• Języki publikacji: EN

Abstrakty

EN

We study the evolution and monotonicity of the eigenvalues of p-Laplace operator on an m-dimen-sional compact Riemannian manifold M whose metric g(t) evolves by the Ricci-harmonic flow. The first nonzero eigenvalue is proved to be monotonically nondecreasing along the flow and differentiable almost everywhere. As a corollary, we recover the corresponding results for the usual Laplace-Beltrami operator when p = 2. We also examine the evolution and monotonicity under volume preserving flow and it turns out that the first eigenvalue is not monotone in general.

Słowa kluczowe

EN

Ricci harmonic flow; eigenvalue; p-Laplacian; monotonicity

PL

przepływ harmoniczny Ricciego; wartość własna; p-Laplacian; monotoniczność

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2015
• Tom: Vol. 21, nr 2
• Strony: 147--160
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Abolarinwa A.

• University of Sussex, Brighton, BN1 9QH, United Kingdom

Bibliografia

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