𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Critical metrics of the eigenvalue gaps of Laplace-Beltrami operators

✍ Scribed by Songbo Hou

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
98 KB
Volume
284
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Let M be a compact smooth manifold of dimension n ⩾ 2. We investigate critical metrics of the Laplacian eigenvalue gaps considered as functionals on the space of Riemannian metrics or a conformal class of metrics on M. We give necessary and sufficient conditions for a metric to be critical for such a functional. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

📜 SIMILAR VOLUMES

Homogenization of eigenvalue problem for
Homogenization of eigenvalue problem for Laplace–Beltrami operator on Riemannian manifold with complicated ‘bubble-like’ microstructure
✍ Andrii Khrabustovskyi 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 151 KB

## Abstract We study the asymptotic behavior of the eigenvalues and the eigenfunctions of the Laplace–Beltrami operator on a Riemannian manifold __M__^ε^ depending on a small parameter ε>0 and whose structure becomes complicated as ε→0. Under a few assumptions on scales of __M__^ε^ we obtain the ho

On the absolutely continuous spectrum of
On the absolutely continuous spectrum of the Laplace–Beltrami operator acting on p -forms for a class of warped product metrics
✍ Francesca Antoci 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 270 KB 👁 1 views

## Abstract We explicitely compute the absolutely continuous spectrum of the Laplace–Beltrami operator for __p__ ‐forms for the class of warped product metrics __dσ__ ^2^ = __y__ ^2__a__^ __dy__ ^2^ + __y__ ^2__b__^ __dθ__ ^2^, where __y__ is a boundary defining function on the unit ball __B__ (0,

On the Eigenvalues of Operators with Gap
On the Eigenvalues of Operators with Gaps. Application to Dirac Operators
✍ Jean Dolbeault; Maria J. Esteban; Eric Séré 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 173 KB

This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator. We prove an abstract theorem, then we apply it to the case of Dirac operators with a Coulomb-like potential. The result is optimal for the Coulomb p