Index and nullity of minimal surfaces via representation theory

@misc{karpukhin2026index,
  title = {{Index and nullity of minimal surfaces via representation theory}},
  author = {Mikhail Karpukhin and Mario B. Schulz},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03023},
  eprint = {2610.03023},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03023},
}

TY  - UNPB
TI  - Index and nullity of minimal surfaces via representation theory
AU  - Mikhail Karpukhin
AU  - Mario B. Schulz
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03023
UR  - https://arxiv.org/abs/2610.03023
AB  - We develop a representation-theoretic approach to determine the Morse index and nullity of an embedded minimal surface based only on its topology and symmetry group. The method combines an equivariant comparison between the second variations of area and energy with the representation theory of the dihedral group. In the Euclidean unit ball we compute for every k≥3 the Morse index and nullity of any free boundary minimal k-noid with prismatic symmetry of order 4k, and of any free boundary minimal surface of genus one with connected boundary and antiprismatic symmetry of order eight. In the round sphere we obtain an alternative computation for the Morse index and nullity for the first family of the Lawson surfaces, using only half of their symmetry group. The results are independent of any particular construction of the surfaces.
ER  -