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We study singularity structure of Yang-Mills flow in dimensions $n geq 4$. First we obtain a description of the singular set in terms of concentration for a localized entropy quantity, which leads to an estimate of its Hausdorff dimension. We develop a theory of tangent measures for the flow, which leads to a stratification of the singular set. By a refined blowup analysis we obtain Yang-Mills connections or solitons as blowup limits at any point in the singular set.
We define a family of functionals generalizing the Yang-Mills functional. We study the corresponding gradient flows and prove long-time existence and convergence results for subcritical dimensions as well as a bubbling criterion for the critical dime
Following work of Colding-Minicozzi, we define a notion of entropy for connections over $mathbb R^n$ which has shrinking Yang-Mills solitons as critical points. As in Colding-Minicozzi, this entropy is defined implicitly, making it difficult to work
We study a new deformed Hermitian Yang-Mills Flow in the supercritical case. Under the same assumption on the subsolution as Collins-Jacob-Yau cite{cjy2020cjm}, we show the longtime existence and the solution converges to a solution of the deformed H
We give a complete description of the global existence and convergence for the Ricci-Yang-Mills flow on $T^k$ bundles over Riemann surfaces. These results equivalently describe solutions to generalized Ricci flow and pluriclosed flow with symmetry.
In this paper, we consider the deformed Hermitian-Yang-Mills equation on closed almost Hermitian manifolds. In the case of hypercritical phase, we derive a priori estimates under the existence of an admissible $mathcal{C}$-subsolution. As an applicat