Systolic extremality conjecture for the singular manifold (B2,g0)(B_2,g_0)

Let (B2,g0)(B_2,g_0) be the singular Riemannian manifold considered in the source. A metric is extremal for the isosystolic inequality if it realizes the optimal systolic constant in its topological manifold. Systolic extremality conjecture. The manifold (B2,g0)(B_2,g_0) is extremal for the isosystolic inequality. The manifold (B2,g0)(B_2,g_0) is singled out because its systolic geodesics cover the manifold for every systolic class, in addition to the abundance of systolic geodesics shared by the other candidate manifolds. The supplied source does not state a resolution of this global extremality claim.

Sources & referencesView supporting material

Primary source

Chady El Mir, “Bavard's systolically extremal Klein bottles and three dimensional applications”, arXiv:1007.0877 (2020).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.