Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

 Siegel der Universität Augsburg

 

Oberseminar Differentialgeometrie

 

Professor Pedro Salomao
Universität Sao Paulo und Universität Bochum
 
spricht am
 
Montag, 9. Juli 2018
 
um
 
16:00 Uhr
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»Sharp systolic inequalities for spheres of revolution«

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 with the same prime period. We also show that the systolic inequality is strictly less than $\pi$ for the non-reversible Finsler metrics induced by the usual Zermelo navigation data on a sphere of revolution.

 

Hierzu ergeht herzliche Einladung.
Urs Frauenfelder
 

Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).


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