Upper Bounds for Eigenvalues of Natural Operators on Compact Riemannian Manifolds, M.Sc. Thesis Sharif University of Technology ; Colbois, Bruno (Supervisor) ; El Soufi, Ahmad (Supervisor) ; Ranjbar-Motlagh, Alireza (Supervisor)
Abstract
The purpose of this thesis is to find upper bounds for the eigenvalues of natural operators acting on functions on a compact Riemannian man-ifold (M, g) such as the Laplace–Beltrami operator and Laplace-type operators. In the case of the Laplace–Beltrami operator, two aspects are investigated:
The first aspect is to study relationships between the intrinsic geometry and eigenvalues of the Laplace–Beltrami operator. In this regard, we obtain upper bounds depending only on the dimension and a conformal invariant called min-conformal volume. Asymptotically, these bounds are consistent with the Weyl law. They improve previous results by Korevaar and Yang and Yau. The proof relies on the... Cataloging briefUpper Bounds for Eigenvalues of Natural Operators on Compact Riemannian Manifolds, M.Sc. Thesis Sharif University of Technology ; Colbois, Bruno (Supervisor) ; El Soufi, Ahmad (Supervisor) ; Ranjbar-Motlagh, Alireza (Supervisor)
Abstract
The purpose of this thesis is to find upper bounds for the eigenvalues of natural operators acting on functions on a compact Riemannian man-ifold (M, g) such as the Laplace–Beltrami operator and Laplace-type operators. In the case of the Laplace–Beltrami operator, two aspects are investigated:
The first aspect is to study relationships between the intrinsic geometry and eigenvalues of the Laplace–Beltrami operator. In this regard, we obtain upper bounds depending only on the dimension and a conformal invariant called min-conformal volume. Asymptotically, these bounds are consistent with the Weyl law. They improve previous results by Korevaar and Yang and Yau. The proof relies on the... Find in contentBookmark |
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