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$p$-Laplacian first eigenvalues controls on Finsler manifolds | | Cyrille Combete
; Serge Degla
; Leonard Todjihounde
; | | Date: |
21 Mar 2017 | | Abstract: | Given a Finsler manifold $(M,F)$, it is proved that the first eigenvalue of
the Finslerian $p$-Laplacian is bounded above by a constant depending on $ p$,
the dimension of $M$, the Busemann-Hausdorff volume and the reversibility
constant of $(M,F)$.
For a Randers manifold $(M,F:=sqrt{g}+eta)$, where $g$ is a Riemannian
metric on $M$ and $eta$ an appropriate $1$-form on $M$, it is shown that the
first eigenvalue $lambda_{1,p}(M,F)$ of the Finslerian $p$-Laplacian defined
by the Finsler metric $F$ is controled by the first eigenvalue
$lambda_{1,p}(M,g)$ of the Riemannian $p$-Laplacian defined on $(M,g)$.
Finally, the Cheeger’s inequality for Finsler Laplacian is extended for
$p$-Laplacian, with $p > 1$. | | Source: | arXiv, 1704.1402 | | Services: | Forum | Review | PDF | Favorites | |
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