稳定Higgs丛的点态能量单调性
Pointwise energy monotonicity for stable Higgs bundles
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中文总结 AI 辅助
研究稳定Higgs丛沿C*-流的能量密度点态单调性猜想，证明秩二成立，秩≥3构造反例，揭示秩依赖性。
中文摘要 AI 辅助
我们研究了Qiongling Li关于稳定SL(n,C) Higgs丛沿C*-流的能量密度点态单调性的猜想。我们证明该猜想在秩二情形下成立：对于每个稳定的SL(2,C) Higgs丛，能量密度沿C*-轨道点态非减。相反，我们表明这一现象确实依赖于秩。对于每个秩n≥3，我们构造了稳定的SL(n,C) Higgs丛，其能量密度沿C*-流不满足单调性。
英文摘要
We study the Dai--Li conjecture concerning the pointwise monotonicity of the energy density along the $\mathbb C^*$-flow of stable $\mathrm{SL}(n,\mathbb C)$ Higgs bundles. We prove that the conjecture holds in rank two: for every stable $\mathrm{SL}(2,\mathbb C)$ Higgs bundle, the energy density is pointwise nondecreasing along the $\mathbb C^*$-orbit. In contrast, we show that this phenomenon is genuinely rank-dependent. For every rank $n\geq 3$, we construct stable $\mathrm{SL}(n,\mathbb C)$ Higgs bundles for which the energy density fails to be monotone along the $\mathbb C^*$-flow.
发表机构
- School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）
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