Buser's conjecture on Bers constants for hyperbolic surfaces

From papers

Let MM be a hyperbolic surface with genus gg and nn cusps. A pants decomposition of MM 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 MM has a pants decomposition in which each curve has length at most

Cg+nC\sqrt{g+n}

for some universal constant CC.

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

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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

No solutions have been posted yet.