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Full text | |
Author(s): |
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 |
Abstract | |
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 |