On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold

John C. Taylor

Annales de l'institut Fourier (1978)

  • Volume: 28, Issue: 2, page 25-52
  • ISSN: 0373-0956

Abstract

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The Martin compactification of a bounded Lipschitz domain D ⊂ R n is shown to be D ‾ for a large class of uniformly elliptic second order partial differential operators on D .Let X be an open Riemannian manifold and let M ⊂ X be open relatively compact, connected, with Lipschitz boundary. Then M ‾ is the Martin compactification of M associated with the restriction to M of the Laplace-Beltrami operator on X . Consequently an open Riemannian manifold X has at most one compactification which is a compact Riemannian manifold with boundary whose interior is X .

How to cite

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Taylor, John C.. "On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold." Annales de l'institut Fourier 28.2 (1978): 25-52. <http://eudml.org/doc/74360>.

@article{Taylor1978,
abstract = {The Martin compactification of a bounded Lipschitz domain $D\subset \{\bf R\}^n$ is shown to be $\overline\{D\}$ for a large class of uniformly elliptic second order partial differential operators on $D$.Let $X$ be an open Riemannian manifold and let $M\subset X$ be open relatively compact, connected, with Lipschitz boundary. Then $\overline\{M\}$ is the Martin compactification of $M$ associated with the restriction to $M$ of the Laplace-Beltrami operator on $X$. Consequently an open Riemannian manifold $X$ has at most one compactification which is a compact Riemannian manifold with boundary whose interior is $X$.},
author = {Taylor, John C.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {25-52},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold},
url = {http://eudml.org/doc/74360},
volume = {28},
year = {1978},
}

TY - JOUR
AU - Taylor, John C.
TI - On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold
JO - Annales de l'institut Fourier
PY - 1978
PB - Association des Annales de l'Institut Fourier
VL - 28
IS - 2
SP - 25
EP - 52
AB - The Martin compactification of a bounded Lipschitz domain $D\subset {\bf R}^n$ is shown to be $\overline{D}$ for a large class of uniformly elliptic second order partial differential operators on $D$.Let $X$ be an open Riemannian manifold and let $M\subset X$ be open relatively compact, connected, with Lipschitz boundary. Then $\overline{M}$ is the Martin compactification of $M$ associated with the restriction to $M$ of the Laplace-Beltrami operator on $X$. Consequently an open Riemannian manifold $X$ has at most one compactification which is a compact Riemannian manifold with boundary whose interior is $X$.
LA - eng
UR - http://eudml.org/doc/74360
ER -

References

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