On Tabachnikov’s conjecture › SPbU Researchers Portal

DOI

https://doi.org/10.1090/S1061-0022-07-00989-2
Final published version

A. I. Nazarov
F. V. Petrov

Tabachnikov’s conjecture is proved: for any closed curve Γ lying inside a convex closed curve Γ₁ the mean absolute curvature T(Γ) exceeds T(Γ₁) if Γ ≠ kΓ₁.

Original language	English
Pages (from-to)	125-135
Number of pages	11
Journal	St. Petersburg Mathematical Journal
Volume	19
Issue number	1
DOIs	https://doi.org/10.1090/S1061-0022-07-00989-2
State	Published - 1 Jan 2008

Scopus subject areas

Analysis

Research areas

Convexity, Geometric inequalities, Mean absolute curvature

ID: 45872515