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Convexity and absolute continuity of the Laplace-Beltrami operator

✍ Scribed by Frederico Xavier

Publisher
Springer
Year
1988
Tongue
English
Weight
363 KB
Volume
282
Category
Article
ISSN
0025-5831

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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,

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## 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