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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A systolic inequality for geodesic flows on the two-sphere

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Abbondandolo, Alberto ; Bramham, Barney ; Hryniewicz, Umberto L. ; Salomao, Pedro A. S.
Total Authors: 4
Document type: Journal article
Source: MATHEMATISCHE ANNALEN; v. 367, n. 1-2, p. 701-753, FEB 2017.
Web of Science Citations: 6

For a Riemannian metric g on the two-sphere, let be the length of the shortest closed geodesic and be the length of the longest simple closed geodesic. We prove that if the curvature of g is positive and sufficiently pinched, then the sharp systolic inequalities l(min)(g)(2) <= pi Area(S-2, g) <= l(max)(g)(2), hold, and each of these two inequalities is an equality if and only if the metric g is Zoll. The first inequality answers positively a conjecture of Babenko and Balacheff. The proof combines arguments from Riemannian and symplectic geometry. (AU)

FAPESP's process: 13/20065-0 - Symplectic dynamics in dimension 3
Grantee:Pedro Antonio Santoro Salomão
Support Opportunities: Regular Research Grants