A note on Makeev's conjectures

Abstract

A counterexample is given for the Knaster-like conjecture of Makeev for functions on $S^2$. Some particular cases of another conjecture of Makeev, on inscribing a quadrangle into a smooth simple closed curve, are solved positively.

Cited by in corpus (2)

• Any cyclic quadrilateral can be inscribed in any closed convex smooth curve
• Quadrilaterals inscribed in convex curves