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PreprintCC BY 4.0arXiv

Improved Index and Intersection bounds for Min-Max Geodesics

  • Lorenzo Sarnataro
  • Douglas Stryker
  • Jared Marx-Kuo
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Abstract

In this note, we show that the sum of the Morse index and number of intersections of min-max geodesics achieving the p-widths of a closed surface are bounded above by p, improving a result from our previous work. A key idea is that deformations coming from vertex desingularization and eigenfunctions of the Jacobi operator on geodesics are sufficiently independent.

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Cite

BibTeXRIS
BibTeX
@misc{sarnataro2026improved,
  title = {{Improved Index and Intersection bounds for Min-Max Geodesics}},
  author = {Lorenzo Sarnataro and Douglas Stryker and Jared Marx-Kuo},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08450},
  eprint = {2611.08450},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08450},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Improved Index and Intersection bounds for Min-Max Geodesics
AU  - Lorenzo Sarnataro
AU  - Douglas Stryker
AU  - Jared Marx-Kuo
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08450
UR  - https://arxiv.org/abs/2611.08450
AB  - In this note, we show that the sum of the Morse index and number of intersections of min-max geodesics achieving the p-widths of a closed surface are bounded above by p, improving a result from our previous work. A key idea is that deformations coming from vertex desingularization and eigenfunctions of the Jacobi operator on geodesics are sufficiently independent.
ER  -