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Covering lemmas and BMO estimates for eigenfunctions on Riemannian surfaces.

Guozhen Lu (1991)

Revista Matemática Iberoamericana

The principal aim of this note is to prove a covering Lemma in R2. As an application of this covering lemma, we can prove the BMO estimates for eigenfunctions on two-dimensional Riemannian manifolds (M2, g). We will get the upper bound estimate for || log |u| ||BMO, where u is the solution to Δu + λu = 0, for λ > 1 and Δ is the Laplacian on (M2, g). A covering lemma on homogeneous spaces is also obtained in this note.

Coverings, heat kernels and spanning trees.

Chung, Fan, Yau, S.-T. (1999)

The Electronic Journal of Combinatorics [electronic only]

Cramér's formula for Heisenberg manifolds

Mahta Khosravi, John A. Toth (2005)

Annales de l'institut Fourier

Let $R (λ)$ be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that $\int_{1}^{T} {| R (t) |}^{2} d t = c T^{\frac{5}{2}} + O_{δ} (T^{\frac{9}{4} + δ})$ , where $c$ is a specific nonzero constant and $δ$ is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that $R (t) = O_{δ} (t^{\frac{3}{4} + δ})$ .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the $2 n + 1$ -dimensional case.

Displaying 121 – 132 of 132

Covering lemmas and BMO estimates for eigenfunctions on Riemannian surfaces.

Coverings, heat kernels and spanning trees.

Cramér's formula for Heisenberg manifolds

Critical diffusions

Critical points at infinity in the variational calculus

Critical points of the steady state of a Fokker-Planck equation.

Crochet de Jacobi non local sur un revêtement et ses applications à l’étude de l’équation de Burgers

Curvature Pinching and Eigenvalue Rigidity for Minimal Submanifolds.

Curved Casimir operators and the BGG machinery.

Cusp Forms and the Index Theorem for Manif olds with Boundary.

Cycles lagrangiens, fonctions constructibles et applications

Cyclic cocycles, renormalization and eta-invariants.

Currently displaying 121 – 132 of 132