A local systolic inequality and Gromov's filling area conjecture

Abstract

The article treats some questions around Gromov's filling area conjecture. It intended to show that any filling with volume $<2\pi$ would not be attained and to show a local systolic inequality, implying an a priori lower estimate on the total volume. The proof of both assertions, the second of which is wrong, suffered from a computational mistake.

8 pages. Withdrawn due to a computational error in the derivation of the main results