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Embedding of open riemannian manifolds by harmonic functions

Robert E. Greene, H. Wu (1975)

Annales de l'institut Fourier

Let M be a noncompact Riemannian manifold of dimension n . Then there exists a proper embedding of M into R 2 n + 1 by harmonic functions on M . It is easy to find 2 n + 1 harmonic functions which give an embedding. However, it is more difficult to achieve properness. The proof depends on the theorems of Lax-Malgrange and Aronszajn-Cordes in the theory of elliptic equations.

Estimation of vibration frequencies of linear elastic membranes

Luca Sabatini (2018)

Applications of Mathematics

The free motion of a thin elastic linear membrane is described, in a simplyfied model, by a second order linear homogeneous hyperbolic system of partial differential equations whose spatial part is the Laplace Beltrami operator acting on a Riemannian 2-dimensional manifold with boundary. We adapt the estimates of the spectrum of the Laplacian obtained in the last years by several authors for compact closed Riemannian manifolds. To make so, we use the standard technique of the doubled manifold to...

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