שלחו לחבר

A geometric inequality for length and volume in complex projective plane

Speaker
Mikhail Katz, Bar-Ilan University
Date
01/12/2019 - 13:00 - 12:00
Place
Department Seminar Room 216/201
Abstract

 

 In the 1950s, Carl Loewner proved an inequality relating the
shortest closed geodesics on a 2-torus to its area.  Many
generalisations have been developed since, by Gromov and others.  We
show that the shortest closed geodesic on an area-minimizing surface S
for a generic metric on CP^2 is controlled by the total volume, even
though the area of S is not.  We exploit the Croke--Rotman inequality,
Gromov's systolic inequalities, the Kronheimer--Mrowka proof of the
Thom conjecture, and White's regularity results for area minimizers.

תאריך עדכון אחרון : 24/11/2019