A priori estimates in geometry and Sobolev spaces on open manifolds

Jürgen Eichhorn

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Nonimmersion results for the real flag manifolds $ℝ F (1, 1, 1, n - 3)$

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Global Gronwall estimates for integral curves on Riemannian manifolds.

Michael Kunzinger, Hermann Schichl, Roland Steinbauer, James A. Vickers (2006)

Revista Matemática Complutense

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We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of roundoff errors. Our results may therefore be seen as a prerequisite for the generalization of such methods to the setting of Riemannian manifolds.

The configuration space of gauge theory on open manifolds of bounded geometry

Jürgen Eichhorn, Gerd Heber (1997)

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We define suitable Sobolev topologies on the space $𝒞_{P} (B_{k}, f)$ 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.