Almost minimizing Yang$-$Mills fields: log-epiperimetric inequality, non-concentration, and uniqueness of tangents

Abstract

We establish a direct log-epiperimetric inequality for Yang$-$Mills fields in arbitrary dimension and we leverage on it to prove uniqueness of tangent cones with isolated singularity for energy minimizing Yang$-$Mills fields and $\ddot{I}‰$-ASD connections (where $\ddot{I}‰$ is not necessarily closed) satisfying some suitable regularity assumptions. En route to this we establish a Luckhaus type lemma for Yang$-$Mills connections to exclude curvature concentration along blow-up sequences.

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