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Eigenvalue estimate for the rough Laplacian on differential forms
Auteur(s)
Maerten, Daniel
Date Issued
2010-2-21
Journal
Manuscripta Math.
Vol.
3-4
No
132
From page
399
To page
413
Abstract
We study the spectrum of the rough Laplacian acting on differential
forms on a compact Riemannian manifold (M,g).
We first construct on M metrics of volume 1 whose spectrum is as large as desired.
Then, provided that the Ricci curvature of g is bounded below,
we relate the spectrum of the rough Laplacian on 1--forms to the spectrum of the Laplacian on functions, and derive some upper bound in agreement with the asymptotic Weyl law.
forms on a compact Riemannian manifold (M,g).
We first construct on M metrics of volume 1 whose spectrum is as large as desired.
Then, provided that the Ricci curvature of g is bounded below,
we relate the spectrum of the rough Laplacian on 1--forms to the spectrum of the Laplacian on functions, and derive some upper bound in agreement with the asymptotic Weyl law.
Identifiers
Publication type
journal article
