Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.13392

Ruling out Infinite-Time Bubbling under $SO(4)$-Equivariant Yang--Mills Flow on $\mathbb{S}^4\times SU(2)$

Gabriel Tribe
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the Yang--Mills flow on $\mathbb{S}^4$ restricted to $\mathrm{SO}(4)$-equivariant connections on the trivial $\mathrm{SU}(2)$ bundle. It was expected that antipodal instanton--anti-instanton configurations would lead to infinite-time singularities along the flow. We show that this does not occur. Moreover, for any smooth equivariant initial condition, the flow converges to the trivial flat connection.

Explore related subjects

math.DG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gabriel Tribe. 2026-10-09. Ruling out Infinite-Time Bubbling under $SO(4)$-Equivariant Yang--Mills Flow on $\mathbb{S}^4\times SU(2)$. https://arxiv.org/abs/2610.13392

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Lojasiewicz inequalities for maps of the 2-sphere

We prove a Lojasiewicz-Simon inequality $$ \left| E(u) - 4πn \right| \leq C \| \mathcal{T}(u) \|^α$$ for maps $u \in W^{2,2}\left( S^2, S^2 \right).$ The inequality holds with $α= 1$ in general and with $α> 1$ unless $u$ is nearly constant on an open set. We obtain polynomial convergence of weak solutions of harmonic map flow $u(t) : S^2 \to S^2$ as $t \to \infty$ on compact domains away from the singular set, assuming that the body map is nonconstant. The proof uses Topping's repulsion estimates together with polynomial lower bounds on the energy density coming from a bubble-tree induction argument.

math.DG↗
arXiv2026

Butcher series for Hamiltonian Poisson integrators through symplectic groupoids

We exhibit a new pre-Lie algebra in the framework of symplectic groupoids and, in turn, use Butcher trees to compute the Taylor series of a solution of a Hamilton-Jacobi equation on any symplectic groupoid $\mathcal{G} \rightrightarrows M.$ The impact of this new algebraic approach is twofold. On the geometric side, it yields algebraic operations to approximate Lagrangian bisections of $\mathcal{G}$ using the Butcher-Connes-Kreimer Hopf algebra and, in turn, aims at a better understanding of the group of Hamiltonian diffeomorphisms of $M.$ On the computational side, we define a new class of Poisson integrators for Hamiltonian dynamics on Poisson manifolds.

math.DG↗
arXiv2026

Urysohn width of hypersurfaces and positive macroscopic scalar curvature

We prove that if a complete Riemannian $n$-manifold with non-trivial codimension 1 homology with $\mathbb{Z}_2$-coefficients or $\mathbb{Z}$-coefficients has positive macroscopic scalar curvature large enough, then it contains a non-nullhomologous hypersurface of small Urysohn $(n-2)$-width. This constitutes a macroscopic analogue of a theorem by Bray--Brendle--Neves on the area of non-contractible 2-spheres in a closed Riemannian 3-manifold with positive scalar curvature. Our proof is based on an adaptation of Guth's macroscopic version of the Schoen-Yau descent argument.

math.DG↗