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PreprintCC BY 4.0arXiv

L2 Curvature Bounds for Area-Minimizing Currents Mod(2)

  • Zachary Lihn
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Abstract

We prove \emph{a priori} interior L2 bounds for the second fundamental form of area-minimizing currents modulo $2$ in every dimension n≥ 2 and arbitrary codimension. The bounds depend only on the dimension, codimension, and an upper bound for the mass. As a corollary, we show that area-minimizing surfaces modulo $2$ with bounded area lie in finitely many diffeomorphism classes. This answers a question of \cite{Liu2020WeakCounterexamples}.

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Cite

BibTeXRIS
BibTeX
@misc{lihn2026curvature,
  title = {{$L^2$ Curvature Bounds for Area-Minimizing Currents Mod(2)}},
  author = {Zachary Lihn},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26592},
  eprint = {2609.26592},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26592},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - L^2 Curvature Bounds for Area-Minimizing Currents Mod(2)
AU  - Zachary Lihn
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26592
UR  - https://arxiv.org/abs/2609.26592
AB  - We prove \emph{a priori} interior L^2 bounds for the second fundamental form of area-minimizing currents modulo $2$ in every dimension n≥ 2 and arbitrary codimension. The bounds depend only on the dimension, codimension, and an upper bound for the mass. As a corollary, we show that area-minimizing surfaces modulo $2$ with bounded area lie in finitely many diffeomorphism classes. This answers a question of \cite{Liu2020WeakCounterexamples}.
ER  -