2014/10/16 by Kelleher, Casey Lynn, Streets, Jeff
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1410.4547
Following work of Colding-Minicozzi, we define a notion of entropy for connections over \mathbb Rn which has shrinking Yang-Mills solitons as critical points. As in Colding-Minicozzi, this entropy is defined implicitly, making it difficult to work with analytically. We prove a theorem characterizing entropy stability in terms of the spectrum of a certain linear operator associated to the soliton. This leads furthermore to a gap theorem for solitons. These results point to a broader strategy of studying "generic singularities" of Yang-Mills flow, and we discuss the differences in this strategy in dimension n=4 versus n ≥ 5.