A. I. Nazarov, F. V. Petrov, “On Tabachnikov's conjecture”, Algebra i Analiz, 2007, Volume 19, Issue 1,Pages <nobr>177

This article is cited in 4 papers

Research Papers

On Tabachnikov's conjecture

A. I. Nazarov^a, F. V. Petrov^b

^a St. Petersburg State University, Department of Mathematics and Mechanics
^b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: Tabachnikov's conjecture is proved: for any closed curve $\Gamma$ lying inside aЁconvex closed curve $\Gamma_1$ the mean absolute curvature $T(\Gamma)$ exceeds $T(\Gamma_1)$ if $\Gamma\ne k\Gamma_1$.

Keywords: Geometric inequalities, mean absolute curvature, convexity.

MSC: Primary 53A04; Secondary 52A40, 52A10

Received: 01.08.2006