New Methods in Finsler Geometry

Sharp systolic inequalities for spheres of revolution

speaker: Pedro Salomao (University of Sao Paulo)

abstract: In a joint work with Abbondandolo, Bramham and Hryniewicz, we study systolic inequalities for spheres of revolution. The systolic ratio of a Riemannian metric on the 2-sphere is defined as the quotient of the square of the length of the shortest closed geodesic by the area. This notion naturally extends to Finsler metrics, considering the Holmes-Thompson area. We show that the systolic ratio of a sphere of revolution S is bounded from above by $\pi$, and is equal to $\pi$ if and only if S is Zoll, that is all of its geodesics are closed and have the same prime period. We also show that the systolic inequality is strictly less than $\pi$ for non-reversible Finsler metrics on S induced by suitable rotational invariant killing vector fields.

timetable:
Fri 25 May, 9:10 - 10:00, Aula Dini
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