A Generalization of a Levitin and Parnovski Universal Inequality for Eigenvalues

2010/12/03 by Saïd Ilias, Ilias, Said, Ola Makhoul +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.1012.0704

Abstract

In this paper, we derive "universal" inequalities for the sums of eigenvalues of the Hodge de Rham Laplacian on Euclidean closed Submanifolds and of eigenvalues of the Kohn Laplacian on the Heisenberg group. These inequalities generalize the Levitin-Parnovski inequality obtained for the sums of eigenvalues of the Dirichlet Laplacian of a bounded Euclidean domain. New Reilly and Asada inequalities are also obtained.

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• A weighted Reilly type integral formula for differential forms and its applications
• The First Eigenvalue of Embedded Minimal Hypersurfaces in the Unit Sphere I: Yau's Conjecture

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