# Uhlenbeck Compactness

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*Katrin Wehrheim*

A publication of the European Mathematical Society

This book gives a detailed account of the analytic foundations of
gauge theory, namely, Uhlenbeck's compactness theorems for general
connections and for Yang-Mills connections. It guides graduate students into
the analysis of Yang-Mills theory as well as serves as a reference for
researchers in the field.

The volume is largely self contained. It contains a number of appendices
(e.g., on Sobolev spaces of maps between manifolds) and an introductory part
covering the \(L^p\)-regularity theory for the inhomogenous Neumann
problem. The two main parts contain the full proofs of Uhlenbeck's weak and
strong compactness theorems on closed manifolds as well as their
generalizations to manifolds with boundary and noncompact manifolds. These
parts include a number of useful analytic tools such as general patching
constructions and local slice theorems.

The book is suitable for graduate students and research mathematicians
interested in differential geometry, global analysis, and analysis on
manifolds.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in differential geometry, global analysis, and analysis on manifolds.