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arXiv · 2504.07054

Weighted Lojasiewicz inequalities and regularity of harmonic map flow

Alex Waldron
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Abstract

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 $S^2,$ yielding both properties in this case.

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Alex Waldron. 2025-04-09. Weighted Lojasiewicz inequalities and regularity of harmonic map flow. https://arxiv.org/abs/2504.07054

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