Buser's conjecture on Bers constants for hyperbolic surfaces
Buser's conjecture on Bers constants for hyperbolic surfaces
Let be a hyperbolic surface with genus and cusps. A pants decomposition of is a finite collection of pairwise disjoint simple closed curves whose complement is a finite union of thrice-punctured hyperbolic spheres.
Buser's conjecture. The surface has a pants decomposition in which each curve has length at most
for some universal constant .
This conjecture concerns the optimal upper bounds for Bers constants of hyperbolic surfaces with cusps. The source does not indicate whether the conjecture has been resolved.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Sources & referencesView supporting material
Primary source
Gregory R. Chambers, “Uryson width and pants decompositions of hyperbolic surfaces”, arXiv:2207.11874 (2022).
Additional references
2 papers in this index state this conjecture (2009–2022). The statement above is taken from the most recent of them; the others are arXiv:0912.1540.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.