On S.L. Tabachnikov's conjecture
Metric Geometry
2007-05-23 v1
Abstract
S. L. Tabachnikov's conjecture is proved: for any closed curve lying inside convex closed curve the mean absolute curvature exceeds if . An inequality is proved for curves in a hemisphere.
Cite
@article{arxiv.math/0507379,
title = {On S.L. Tabachnikov's conjecture},
author = {A. I. Nazarov and F. V. Petrov},
journal= {arXiv preprint arXiv:math/0507379},
year = {2007}
}