Contents

• Isoperimetric inequality
• Pu's inequality
• Loewner's torus inequality
• Stable norm and stable systoles
• Gromov's inequality for complex projective space
• Other inequalities due to Gromov
• Bibliography

Each of the sections below should not take more than 60 seconds to read and understand (with the possible exception of the proof in Section 5). Please contact katzmik at macs.deletethis.biu.andthis.ac.il for clarifications.