Riemannian manifolds with maximal eigenfunction growth
نویسندگان
چکیده
منابع مشابه
Riemannian Manifolds with Maximal Eigenfunction Growth
On any compact Riemannian manifold (M,g) of dimension n, the Lnormalized eigenfunctions {φλ} satisfy ||φλ||∞ ≤ Cλ n−1 2 where −∆φλ = λ 2φλ. The bound is sharp in the class of all (M, g) since it is obtained by zonal spherical harmonics on the standard n-sphere S. But of course, it is not sharp for many Riemannian manifolds, e.g. flat tori R/Γ. We say that S, but not R/Γ, is a Riemannian manifol...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2002
ISSN: 0012-7094
DOI: 10.1215/s0012-7094-02-11431-8