On the Injectivity of Mean Value Mapping between Convex Quadrilaterals

TL;DR

This paper proves that the mean value mapping between convex quadrilaterals is injective, confirming a previously conjectured property and contributing to the understanding of geometric mappings in convex polygons.

Contribution

It provides a rigorous proof of the injectivity of mean value mappings specifically for convex quadrilaterals, resolving an open conjecture.

Findings

Mean value mapping is injective for convex quadrilaterals

Confirmed conjecture from Floater and Kosinka (2010)

Advances understanding of geometric mappings in convex polygons

Abstract

We prove that Mean Value mapping between convex quadrilaterals is injective, affirmatively proving a conjecture stated in M. S. Floater and J. Kosinka, On the injectivity of Wachspress and mean value mappings between convex polygons, Adv. in Comp. Math. 32 (2010), 163-174.