Riemannian manifolds with maximal eigenfunction growth

Christopher D. Sogge

Displaying similar documents to “Riemannian manifolds with maximal eigenfunction growth”

The Poisson summation formula for a Dirichlet problem with gliding and glancing rays

M. J. Bennett, F. G. Friedlander (1982)

Journées équations aux dérivées partielles

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Geodesic graphs on special 7-dimensional g.o. manifolds

Zdeněk Dušek, Oldřich Kowalski (2006)

Archivum Mathematicum

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In ( Dušek, Z., Kowalski, O. and Nikčević, S. Ž., New examples of Riemannian g.o. manifolds in dimension 7, Differential Geom. Appl. 21 (2004), 65–78.), the present authors and S. Nikčević constructed the 2-parameter family of invariant Riemannian metrics on the homogeneous manifolds $M = [SO (5) \times SO (2)] / U (2)$ and $M = [SO (4, 1) \times SO (2)] / U (2)$ . They proved that, for the open dense subset of this family, the corresponding Riemannian manifolds are g.o. manifolds which are not naturally reductive. Now we are going to investigate the remaining...

Sub-riemannian sphere in Martinet flat case

A. Agrachev, B. Bonnard, M. Chyba, I. Kupka (1997)

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Maximally degenerate laplacians

Steven Zelditch (1996)

Annales de l'institut Fourier

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The Laplacian $Δ_{g}$ of a compact Riemannian manifold $(M, g)$ is called if its eigenvalue multiplicity function $m_{g} (k)$ is of maximal growth among metrics of the same dimension and volume. Canonical spheres $(S^{n}, can)$ and CROSSes are MD, and one asks if they are the only examples. We show that a MD metric must be at least a Zoll metric with just one distinct eigenvalue in each cluster, and hence with all band invariants equal to zero. The principal band invariant is then calculated in terms of geodesic integrals...

Tetra and Didi, the cosmic spectral twins.

Doyle, Peter G., Rossetti, Juan Pablo (2004)

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On the spectrum of Riemannian submersions with totally geodesic fibers

Gérard Besson, Manlio Bordoni (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this Note we give a rule to compute explicitely the spectrum and the eigenfunctions of the total space of a Riemannian submersion with totally geodesic fibers, in terms of the spectra and eigenfunctions of the typical fiber and any associated principal bundle.