Alex Waldron

collaborators

6 papers

math.DG2026

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 $SU (r)$ -bundle over a locally hyperKÃ¤hler ALE 4-manifold. Our main result is a noncompact vers…

math.DG2026

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…

math.DG2026

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…

math.DG2026

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 $SU (r)$ -bundle of charge $I^º$ over the 4-sphere, we show that the space of…

math.DG2025

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…

math.DG2025

Lojasiewicz inequalities for maps of the 2-sphere

Alex Waldron

We prove a Lojasiewicz-Simon inequality $E (u) - 4 I ¨ n \leq C ∥ T (u) ∥^{I^} \pm$ for maps $u \in W^{2, 2} (S^{2}, S^{2}) .$ The inequality holds with $Î…