Embedding of open riemannian manifolds by harmonic functions

Robert E. Greene; H. Wu

Annales de l'institut Fourier (1975)

  • Volume: 25, Issue: 1, page 215-235
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Greene, Robert E., and Wu, H.. "Embedding of open riemannian manifolds by harmonic functions." Annales de l'institut Fourier 25.1 (1975): 215-235. <http://eudml.org/doc/74211>.

@article{Greene1975,
abstract = {Let $M$ be a noncompact Riemannian manifold of dimension $n$. Then there exists a proper embedding of $M$ into $\{\bf R\}^\{2n+1\}$ 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.},
author = {Greene, Robert E., Wu, H.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {1},
pages = {215-235},
publisher = {Association des Annales de l'Institut Fourier},
title = {Embedding of open riemannian manifolds by harmonic functions},
url = {http://eudml.org/doc/74211},
volume = {25},
year = {1975},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 25
IS - 1
SP - 215
EP - 235
AB - Let $M$ be a noncompact Riemannian manifold of dimension $n$. Then there exists a proper embedding of $M$ into ${\bf R}^{2n+1}$ 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.
LA - eng
UR - http://eudml.org/doc/74211
ER -

References

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Citations in EuDML Documents

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  1. Dennis M. Deturck, Jerry L. Kazdan, Some regularity theorems in riemannian geometry
  2. Barbara Drinovec Drnovšek, On proper discs in complex manifolds
  3. R. W. R. Darling, Martingales in manifolds. Definition, examples and behaviour under maps
  4. Luc Lemaire, Existence des applications harmoniques et courbure des variétés
  5. Bent Fuglede, Harmonic morphisms between riemannian manifolds
  6. Christine Laurent-Thiébaut, Jürgen Leiterer, Finiteness and separation theorems for Dolbeault cohomologies with support conditions
  7. Paul Baird, Harmonic morphisms and circle actions on 3- and 4-manifolds
  8. Terence Napier, Mohan Ramachandran, The Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds
  9. Terrence Napier, Mohan Ramachandran, Generically strongly q -convex complex manifolds

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