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The Dry Ten Martini Problem for subcritical Type I operators
Abstract
We supply the details of the subcritical dry Ten Martini statement announced in [6, Remark 1.3]: for every irrational frequency, every subcritical Type I energy with resonant rotation number is an endpoint of an open spectral gap. The proof combines the all-frequency Puig argument developed there with quantitative almost reducibility. A different proof was recently given by Li [7].
Related
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- The Brezis-Nirenberg-type problem for critical cooperative and non-cooperative elliptic systems with general subcritical perturbations
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BibTeX
@misc{ge2026martini,
title = {{The Dry Ten Martini Problem for subcritical Type I operators}},
author = {Lingrui Ge},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37438},
eprint = {2609.37438},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37438},
}
RIS
TY - UNPB
TI - The Dry Ten Martini Problem for subcritical Type I operators
AU - Lingrui Ge
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37438
UR - https://arxiv.org/abs/2609.37438
AB - We supply the details of the subcritical dry Ten Martini statement announced in [6, Remark 1.3]: for every irrational frequency, every subcritical Type I energy with resonant rotation number is an endpoint of an open spectral gap. The proof combines the all-frequency Puig argument developed there with quantitative almost reducibility. A different proof was recently given by Li [7].
ER -