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arXiv · 2611.08450

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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Lorenzo Sarnataro, Douglas Stryker, Jared Marx-Kuo. 2026-11-05. Improved Index and Intersection bounds for Min-Max Geodesics. https://arxiv.org/abs/2611.08450

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