Type-I Blowup Solutions for Yang-Mills Flow

2024/11/28 by Kim, Jaehwan, Lee, Sanghoon
#53E99 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.19293

Abstract

In this paper, we construct an infinite-dimensional family of solutions for the Yang-Mills flow on ℝⁿ × SO(n) for 5 ≤ n ≤ 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.

Related

• Singularity formation in the Yang-Mills flow
• Stable blowup for the supercritical Yang-Mills heat flow
• Stabilities of homothetically shrinking Yang-Mills solitons
• Stable blow-up solutions for the SO(d)-equivariant supercritical Yang-Mills heat flow
• Non-self similar blowup solutions to the higher dimensional Yang-Mills heat flows