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Pointwise energy monotonicity for stable Higgs bundles

  • Tianzhi Hu
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Abstract

We study the Dai--Li conjecture concerning the pointwise monotonicity of the energy density along the ℂ*-flow of stable SL(n,ℂ) Higgs bundles. We prove that the conjecture holds in rank two: for every stable SL(2,ℂ) Higgs bundle, the energy density is pointwise nondecreasing along the ℂ*-orbit. In contrast, we show that this phenomenon is genuinely rank-dependent. For every rank n≥ 3, we construct stable SL(n,ℂ) Higgs bundles for which the energy density fails to be monotone along the ℂ*-flow.

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Cite

BibTeXRIS
BibTeX
@misc{hu2026pointwise,
  title = {{Pointwise energy monotonicity for stable Higgs bundles}},
  author = {Tianzhi Hu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35278},
  eprint = {2609.35278},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35278},
}
RIS
TY  - UNPB
TI  - Pointwise energy monotonicity for stable Higgs bundles
AU  - Tianzhi Hu
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.35278
UR  - https://arxiv.org/abs/2609.35278
AB  - We study the Dai--Li conjecture concerning the pointwise monotonicity of the energy density along the ℂ^*-flow of stable SL(n,ℂ) Higgs bundles. We prove that the conjecture holds in rank two: for every stable SL(2,ℂ) Higgs bundle, the energy density is pointwise nondecreasing along the ℂ^*-orbit. In contrast, we show that this phenomenon is genuinely rank-dependent. For every rank n≥ 3, we construct stable SL(n,ℂ) Higgs bundles for which the energy density fails to be monotone along the ℂ^*-flow.
ER  -