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PreprintarXiv licencearXiv

Sharp Sobolev inequalities on minimal immersions via optimal transport

  • Zhe-Feng Xu
  • Zhuo-Nan Zhu
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Abstract

We prove that, for 2≤ p<n, the optimal Lp-Sobolev constant on every complete n-dimensional Euclidean minimal immersion without boundary is the Euclidean Aubin--Talenti constant. The proof combines optimal transport to a suitably chosen target with a two-kernel comparison linking the tangential transport moment to deficits in the normal-fibre and Jacobian estimates.

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Cite

BibTeXRIS
BibTeX
@misc{xu2026sharp,
  title = {{Sharp Sobolev inequalities on minimal immersions via optimal transport}},
  author = {Zhe-Feng Xu and Zhuo-Nan Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13052},
  eprint = {2610.13052},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13052},
}
RIS
TY  - UNPB
TI  - Sharp Sobolev inequalities on minimal immersions via optimal transport
AU  - Zhe-Feng Xu
AU  - Zhuo-Nan Zhu
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13052
UR  - https://arxiv.org/abs/2610.13052
AB  - We prove that, for 2≤ p<n, the optimal L^p-Sobolev constant on every complete n-dimensional Euclidean minimal immersion without boundary is the Euclidean Aubin--Talenti constant. The proof combines optimal transport to a suitably chosen target with a two-kernel comparison linking the tangential transport moment to deficits in the normal-fibre and Jacobian estimates.
ER  -