### Lokale Geometrie des Radius in Riemannschen Mannigfaltigkeiten II

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Introduction. For bounded domains in ${R}^{n}$ satisfying the cone condition there are many embedding and module structure theorem for Sobolev spaces which are of great importance in solving partial differential equations. Unfortunately, most of them are wrong on arbitrary unbounded domains or on open manifolds. On the other hand, just these theorems play a decisive role in foundations of nonlinear analysis on open manifolds and in solving partial differential equations. This was pointed out by the author...

We give an introduction into and exposition of Seiberg-Witten theory.

We define suitable Sobolev topologies on the space ${\mathcal{C}}_{P}({B}_{k},f)$ of connections of bounded geometry and finite Yang-Mills action and the gauge group and show that the corresponding configuration space is a stratified space. The underlying open manifold is assumed to have bounded geometry.

[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 ${\overline{\mathcal{C}}}_{P}^{k}$ 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...

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