Bounds for Eigenvalues of q-Laplacian on Contact Submanifolds of Sasakian Space Forms
Yanlin Li, Fatemah Mofarreh, Abimbola Abolarinwa, Norah Alshehri, Akram Ali
Abstract
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 (l+1)-dimensional special contact slant submanifolds in a Sasakian space form, M˜2k+1(ϵ), with a constant ψ1-sectional curvature, ϵ. From our main results, we recovered the Reilly-type inequalities, which were proven before this study.
Topics & Concepts
Laplace operatorEigenvalues and eigenvectorsMathematicsSectional curvatureMean curvatureMathematical analysisConstant (computer programming)CurvatureSpace formSpace (punctuation)Pure mathematicsOperator (biology)Scalar curvatureGeometryPhysicsComputer scienceSubmanifoldQuantum mechanicsBiochemistryTranscription factorChemistryOperating systemGeneRepressorProgramming languageGeometric Analysis and Curvature FlowsNonlinear Partial Differential EquationsSpectral Theory in Mathematical Physics