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arXiv · 2608.20272

Optimal regularity of stable harmonic maps to spheres

Xuanyu Li
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Abstract

In this paper, we show that the codimension of the singular set of a stable stationary harmonic map to a round $k$-sphere is at least $k+1$ when $k$ is between 3 and 6, and is at least 7 when $k$ is at least 7. The result is sharp in the sense that there exist energy minimizing 0-homogeneous maps in the aforementioned critical dimensions. We also establish non-trivial index bounds for the non-constant harmonic maps from $n$-spheres to $k$-spheres, provided that $n$ is less than $k$.

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Xuanyu Li. 2026-08-20. Optimal regularity of stable harmonic maps to spheres. https://arxiv.org/abs/2608.20272

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