ﻻ يوجد ملخص باللغة العربية
In the spirit of recent work of Lamm, Malchiodi and Micallef in the setting of harmonic maps, we identify Yang-Mills connections obtained by approximations with respect to the Yang-Mills {alpha}-energy. More specifically, we show that for the SU(2) Hopf fibration over the four sphere, for sufficiently small {alpha} values the SO(4) invariant ADHM instanton is the unique {alpha}-critical point which has Yang-Mills {alpha}-energy lower than a specific threshold.
On a Riemannian manifold of dimension $n$ we extend the known analytic results on Yang-Mills connections to the class of connections called $Omega$-Yang-Mills connections, where $Omega$ is a smooth, not necessarily closed, $(n-4)$-form. Special cases
We investigate stability of pullback bundles with respect to adiabatic classes on the total space of holomorphic submersions. We show that the pullback of a stable (resp. unstable) bundle remains stable (resp. unstable) for these classes. Assuming th
We prove a conformally invariant estimate for the index of Schrodinger operators acting on vector bundles over four-manifolds, related to the classical Cwikel-Lieb-Rozenblum estimate. Applied to Yang-Mills connections we obtain a bound for the index
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
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