### The Automorphism Groups of Strongly Pseudoconvex Domains.

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Let $M$ be a noncompact Riemannian manifold of dimension $n$. Then there exists a proper embedding of $M$ into ${\mathbf{R}}^{2n+1}$ by harmonic functions on $M$. It is easy to find $2n+1$ 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.

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