Bounds for Eigenvalues of q-Laplacian on Contact Submanifolds of Sasakian Space Forms - Yanlin Li; Fatemah Mofarreh; Abimbola Abolarinwa; Norah Alshehri; Akram Ali (Mathematics, 2023)
This study establishes new upper bounds for the mean curvature and constant sectional curvature on Riemannian manifolds for the first positive eigenvalue of the q-Laplacian. In particular, various estimates are provided for the first eigenvalue of the q-Laplace operator on closed orientated <semantics>(l+1)</semantics>-dimensional special contact slant submanifolds in a Sasakian space form, <semantics><mover accent="true">M˜</mover>2k+1(ϵ)</semantics>, with a constant <semantics>ψ1</semantics>-sectional curvature, <semantics>ϵ</semantics>. From our main results, we recovered the Reilly-type inequalities, which were proven before this study.