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PreprintCC BY 4.0arXiv

Minimal immersions by first eigenfunctions of Riemann surfaces with large conformal automorphism groups. The Klein quartic

  • Antonio Ros
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Abstract

Minimal immersions of closed surfaces into spheres by first eigenfunctions play an important role in both the theory of minimal surfaces and spectral geometry. In this paper, we establish the existence of equivariant conformal minimal immersions of this type for Hurwitz surfaces and other families of %Riemann surfaces with large automorphism group. Finally, we explicitly construct a conformal minimal equivariant immersion of the Klein quartic into the unit sphere S7 by first eigenfunctions. Ths immersion is a natural candidate for maximizing the normalized λ1 among closed genus-3 surfaces.

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Cite

BibTeXRIS
BibTeX
@misc{ros2026minimal,
  title = {{Minimal immersions by first eigenfunctions of Riemann surfaces with large conformal automorphism groups. The Klein quartic}},
  author = {Antonio Ros},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25592},
  eprint = {2610.25592},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25592},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Minimal immersions by first eigenfunctions of Riemann surfaces with large conformal automorphism groups. The Klein quartic
AU  - Antonio Ros
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25592
UR  - https://arxiv.org/abs/2610.25592
AB  - Minimal immersions of closed surfaces into spheres by first eigenfunctions play an important role in both the theory of minimal surfaces and spectral geometry. In this paper, we establish the existence of equivariant conformal minimal immersions of this type for Hurwitz surfaces and other families of %Riemann surfaces with large automorphism group. Finally, we explicitly construct a conformal minimal equivariant immersion of the Klein quartic into the unit sphere S^7 by first eigenfunctions. Ths immersion is a natural candidate for maximizing the normalized λ_1 among closed genus-3 surfaces.
ER  -