27 citations · 32 across the 12 of their papers we have counts for
13 papers
Convergence of the Yang-Mills flow on ALE gravitational instantons
Anuk Dayaprema, Alex Waldron
We prove a sharp convergence theorem for the Yang-Mills flow on an -bundle over a locally hyperKähler ALE 4-manifold. Our main result is a noncompact versi…
The Yang-Mills equation near instanton-anti-instanton configurations
Alex Waldron, Hao Yin
We study the question of whether a sequence of non-instanton Yang-Mills connections can limit to a bubbling configuration composed only of instantons. In the case that the Uhlenbec…
Integrable Deformations and Stability of the Ricci Flow
Maxwell Stolarski, Alex Waldron
We provide a comparatively simple proof of the dynamical stability of Ricci flow near a linearly stable Ricci-flat ALE metric with integrable deformations. Our proof relies on the…
Weighted Lojasiewicz inequalities and regularity of harmonic map flow
Alex Waldron
At a finite-time singularity of harmonic map flow in the critical dimension, we show that a Lojasiewicz inequality between the quantities appearing in Struwe's monotonicity formula…
Parabolic gap theorems for the Yang-Mills energy
Anuk Dayaprema, Alex Waldron
We prove parabolic versions of several known gap theorems in classical Yang-Mills theory. On an -bundle of charge over the 4-sphere, we show that the space of a…
Lojasiewicz inequalities for maps of the 2-sphere
Alex Waldron
We prove a Lojasiewicz-Simon inequality for maps The inequality holds with $α=…
Strict type-II blowup in harmonic map flow
Alex Waldron
A finite-time singularity of 2D harmonic map flow will be called "strictly type-II" if the outer energy scale satisfies We prove that the body…
Harmonic map flow for almost-holomorphic maps
Chong Song, Alex Waldron
Let be a compact oriented surface and a compact Kähler manifold with nonnegative holomorphic bisectional curvature. For a solution of harmonic map flow starting from an alm…
-instantons on the 7-sphere
Alex Waldron
We study the deformation theory of -instantons on the 7-sphere, specifically those obtained from instantons on the 4-sphere via the quaternionic Hopf fibration. We fi…
Yang-Mills flow on special-holonomy manifolds
Goncalo Oliveira, Alex Waldron
This paper develops Yang-Mills flow on Riemannian manifolds with special holonomy. By analogy with the second-named author's thesis, we find that a supremum bound on a certain curv…
Uhlenbeck compactness for Yang-Mills flow in higher dimensions
Alex Waldron
This paper proves a general Uhlenbeck compactness theorem for sequences of solutions of Yang-Mills flow on Riemannian manifolds of dimension including rectifiability of…
Long-time existence for Yang-Mills flow
Alex Waldron
We establish that finite-time singularities do not occur in four-dimensional Yang-Mills flow, confirming the conjecture of Schlatter, Struwe, and Tahvildar-Zadeh. The proof relies…
Instantons and singularities in the Yang-Mills flow
Alex Waldron
Several results on existence and convergence of the Yang-Mills flow in dimension four are given. We show that a singularity modeled on an instanton cannot form within finite time.…