Bounds for Eigenfunctions of the Laplacian on Compact Riemannian Manifolds
By H. Donnelly. 2001
47 citations recorded by the source corpus.
Suppose that φ is an eigenfunction of −Δ with eigenvalue λ≠0. It is proved that ‖φ‖∞⩽c1λn−14 ‖φ‖2, where n is the dimension of M and c1 depends only upon a bound for the absolute value of the sectional curvature of M and a lower bound for the injectivity radius of M. It is then shown that if M admits an isometric circle action, and the metric is generic, one has exceptional sequences of eigenfunctions satisfying the complementary bounds ‖φk‖∞⩾c2λn−18k ‖φ‖2.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/baf9d9de8795287a23d4db3b53cb0594af8f5ff7
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Geometry and Topology
- Steve Zelditch
- J. Toth
- Zhiqin Lu
- Bernard Shiffman
- Kento Fujita
- Chin-Yu Hsiao
- Robert J. Berman
- G. Marinescu
Citations in the corpus
- Lp Norms of Eigenfunctions in the Completely Integrable Case (2002, result): “leaves correspond to closed geodesics which are invariant under the Rn action. In such cases, the estimate improves to kϕkkL∞ ≥ C(ǫ)λ n−1 4 −ǫ k .This estimate agrees with a recent result of Donnelly [D] on blow-up rates of L∞ norms of eigenfunctions on compact (M,g) with isometric S1 actions. He fin”