Invariance properties of the Laplace operator

Eichhorn, Jürgen. "Invariance properties of the Laplace operator." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1990. [35]-47. <http://eudml.org/doc/220093>.

@inProceedings{Eichhorn1990,
abstract = {[For the entire collection see Zbl 0699.00032.] The paper deals with a special problem of gauge theory. In his previous paper [The invariance of Sobolev spaces over noncompact manifolds, Partial differential equations, Proc. Symp., Holzhaus/GDR 1988, Teubner- Texte Math. 112, 73-107 (1989; Zbl 0681.58011)], the author introduced the Sobolev completions $\bar\{\mathcal \{C\}\}^k_P$ of the space $\{\mathcal \{C\}\}_P$ of all G-connections on a G-principal fibre bundle P. In the present paper, under the assumption of bounded curvatures and their covariant derivatives up to order k, the closedness of the subspace im $\nabla ^\{\omega \}$ is proved to be a property of the whole component comp($\omega $) of a connection $\omega \in \{\mathcal \{C\}\}_P$ in the completion $\bar\{\mathcal \{C\}\}^k_P$. The result follows from the fact that the essential spectrum of the Laplacian $\Delta ^\{\omega \}$ is the same for all $\omega $ lying in the mentioned component.},
author = {Eichhorn, Jürgen},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
keywords = {Geometry; Physics; Proceedings; Winter school; Srní (Czechoslovakia)},
location = {Palermo},
pages = {[35]-47},
publisher = {Circolo Matematico di Palermo},
title = {Invariance properties of the Laplace operator},
url = {http://eudml.org/doc/220093},
year = {1990},
}

TY - CLSWK
AU - Eichhorn, Jürgen
TI - Invariance properties of the Laplace operator
T2 - Proceedings of the Winter School "Geometry and Physics"
PY - 1990
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [35]
EP - 47
AB - [For the entire collection see Zbl 0699.00032.] The paper deals with a special problem of gauge theory. In his previous paper [The invariance of Sobolev spaces over noncompact manifolds, Partial differential equations, Proc. Symp., Holzhaus/GDR 1988, Teubner- Texte Math. 112, 73-107 (1989; Zbl 0681.58011)], the author introduced the Sobolev completions $\bar{\mathcal {C}}^k_P$ of the space ${\mathcal {C}}_P$ of all G-connections on a G-principal fibre bundle P. In the present paper, under the assumption of bounded curvatures and their covariant derivatives up to order k, the closedness of the subspace im $\nabla ^{\omega }$ is proved to be a property of the whole component comp($\omega $) of a connection $\omega \in {\mathcal {C}}_P$ in the completion $\bar{\mathcal {C}}^k_P$. The result follows from the fact that the essential spectrum of the Laplacian $\Delta ^{\omega }$ is the same for all $\omega $ lying in the mentioned component.
KW - Geometry; Physics; Proceedings; Winter school; Srní (Czechoslovakia)
UR - http://eudml.org/doc/220093
ER -