Calculus of Variations and Geometric Measure Theory
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Workshop MAR: Metric Analysis and Regularity

Energy Identity for Stationary Yang Mills connections

Daniele Valtorta

created by dimarino on 18 Sep 2018

Abstract.

In this seminar we present some new results about Yang-Mills connections proved in collaboration with Aaron Naber. In particular, we prove that given a stationary Yang Mills connection with finite energy, there is a uniform $L^1$ bound for its hessian in the interior of the domain. In turn, we also prove the energy quantization conjecture.

The results are based on the quantitative stratification technique and summability estimates for the hessian on annular regions carried out using harmonic gauges. The results are available at arXiv:1610.02898.

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