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Exact formula for the minimal length of a geodesic with at least k self-intersections
Let $M_k$ be the infimum of lengths of geodesics with self-intersection number at least $k$ among all finite-type hyperbolic surfaces. A minimal-length geodesic conjecture asserts…
Conjectureopenclosed-geodesics hyperbolic-geometry self-intersectionarXiv posted 2 days ago
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Chas–Phillips conjecture on maximal self-intersection of odd-length curves on a pair of pants
Chas–Phillips conjecture. The maximal self-intersection number of a closed curve of odd combinatorial length $L(\gamma)$ is
Conjectureopencurves-on-surfaces pair-of-pants self-intersectionarXiv posted 2 days ago
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Whitney's self-intersection conjecture for embedded nonorientable surfaces
Whitney's conjecture. The self-intersection number $[\Sigma^j]^2$ could only take the values
Conjectureopen4-manifolds self-intersection surface-embeddingsarXiv posted 2 days ago

Exact formula for the minimal length of a geodesic with at least k self-intersections