Displaying similar documents to “Normal form of the wave group and inverse spectral theory”

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...

Existence of permanent and breaking waves for a shallow water equation : a geometric approach

Adrian Constantin (2000)

Annales de l'institut Fourier

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The existence of global solutions and the phenomenon of blow-up of a solution in finite time for a recently derived shallow water equation are studied. We prove that the only way a classical solution could blow-up is as a breaking wave for which we determine the exact blow-up rate and, in some cases, the blow-up set. Using the correspondence between the shallow water equation and the geodesic flow on the manifold of diffeomorphisms of the line endowed with a weak Riemannian structure,...