On exponential Yang-Mills connections
Following ideas which have been developed in harmonic map theory the authors introduce the exponential Yang-Mills functional \[ YM_e (\nabla) = \int_M \text{exp} \left( {1\over 2} |R^\nabla |^2 \right) dvg \] defined on the space of all smooth connections \(\nabla\) of a vector bundle \(E\) over a compact Riemannian manifold \((M,g)\). Here \(R^\nabla\) denotes the curvature tensor of the connection \(\nabla\). It is shown that \(YM_e\) admits a minimizing connection \(\nabla\), which is \(\alpha\)-Hölder continuous for all \(0 < \alpha < 1\). Moreover, various properties of exponential Yang-Mills connections (i.e., extremals of \(YM_e\),) are studied.
scientific article; zbMATH DE number 806361
scientific article