Type-I Blowup Solutions for Yang-Mills Flow

TL;DR

This paper constructs a broad family of solutions to the Yang-Mills flow on high-dimensional spaces, demonstrating the existence of asymmetric Type-I blowup solutions and analyzing their convergence to shrinking solitons.

Contribution

It introduces an infinite-dimensional family of solutions for the Yang-Mills flow on d7d7, showing the existence of asymmetric Type-I blowup solutions and their convergence properties.

Findings

Existence of an infinite-dimensional family of solutions.

Construction of asymmetric Type-I blowup solutions.

Convergence to SO(n)-equivariant shrinking solitons.

Abstract

In this paper, we construct an infinite-dimensional family of solutions for the Yang-Mills flow on $\mathbb{R}^n \times SO(n)$ for $5 \leq n \leq 9$, which converge to $SO(n)$-equivariant homothetically shrinking solitons, modulo the gauge group. As a corollary, we prove the existence of asymmetric Type-I blowup solutions for the Yang-Mills flow.