Displaying similar documents to “Isospectral flat orientable 2-orbifolds.”

Boundary volume and length spectra of Riemannian manifolds: what the middle degree Hodge spectrum doesn't reveal

Carolyn S. Gordon, Juan Pablo Rossetti (2003)

Annales de l'Institut Fourier

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Let M be a 2 m -dimensional compact Riemannian manifold. We show that the spectrum of the Hodge Laplacian acting on m -forms does not determine whether the manifold has boundary, nor does it determine the lengths of the closed geodesics. Among the many examples are a projective space and a hemisphere that have the same Hodge spectrum on 1- forms, and hyperbolic surfaces, mutually isospectral on 1-forms, with different injectivity radii. The Hodge m -spectrum also does not distinguish orbifolds...

A priori estimates in geometry and Sobolev spaces on open manifolds

Jürgen Eichhorn (1992)

Banach Center Publications

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Introduction. For bounded domains in R n satisfying the cone condition there are many embedding and module structure theorem for Sobolev spaces which are of great importance in solving partial differential equations. Unfortunately, most of them are wrong on arbitrary unbounded domains or on open manifolds. On the other hand, just these theorems play a decisive role in foundations of nonlinear analysis on open manifolds and in solving partial differential equations. This was pointed out...