到球面的稳定调和映射的最优正则性
Optimal regularity of stable harmonic maps to spheres
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中文总结 AI 辅助
本文研究到球面的稳定调和映射的正则性，确定其奇异集余维数的下界，证明结果最优，并给出n小于k时n维到k维球面非常数调和映射的非平凡指标界。
中文摘要 AI 辅助
本文证明，当k介于3到6之间时，到k维单位球面的稳定稳态调和映射的奇异集余维数至少为k+1；当k≥7时，奇异集余维数至少为7。该结果是最优的，因为在上述临界维数中存在能量极小的0齐次映射。我们还建立了从n维球面到k维球面的非常数调和映射的非平凡指标界，前提是n小于k。
英文摘要
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 $k$.
