2025/04/09 by Alex Waldron, Waldron, Alex
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2504.07054
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 implies continuity of the body map and the no-neck property for bubble-tree decompositions. We prove such an inequality when the target is S2, yielding both properties in this case.