Soit une variété riemannienne non compacte à dimensions. Alors il existe un plongement régulier et propre , de dans tel que les fonctions sont harmoniques sur . Il est facile de trouver fonctions harmoniques qui donnent un plongement régulier. Pour obtenir une telle application qui est à la fois propre, c’est plus subtil. On utilise les théorèmes de Lax-Malgrange et Aronszajn-Cordes dans la théorie d’équations elliptiques.
Let be a noncompact Riemannian manifold of dimension . Then there exists a proper embedding of into by harmonic functions on . It is easy to find 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.
@article{AIF_1975__25_1_215_0, author = {Greene, Robert E. and Wu, H.}, title = {Embedding of open riemannian manifolds by harmonic functions}, journal = {Annales de l'Institut Fourier}, pages = {215--235}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {25}, number = {1}, year = {1975}, doi = {10.5802/aif.549}, mrnumber = {52 #3583}, zbl = {0307.31003}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.549/} }
TY - JOUR AU - Greene, Robert E. AU - Wu, H. TI - Embedding of open riemannian manifolds by harmonic functions JO - Annales de l'Institut Fourier PY - 1975 SP - 215 EP - 235 VL - 25 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.549/ DO - 10.5802/aif.549 LA - en ID - AIF_1975__25_1_215_0 ER -
%0 Journal Article %A Greene, Robert E. %A Wu, H. %T Embedding of open riemannian manifolds by harmonic functions %J Annales de l'Institut Fourier %D 1975 %P 215-235 %V 25 %N 1 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.549/ %R 10.5802/aif.549 %G en %F AIF_1975__25_1_215_0
Greene, Robert E.; Wu, H. Embedding of open riemannian manifolds by harmonic functions. Annales de l'Institut Fourier, Tome 25 (1975) no. 1, pp. 215-235. doi : 10.5802/aif.549. http://archive.numdam.org/articles/10.5802/aif.549/
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