We give necessary and sufficent conditions for a smooth, generic, differential one-form w on Rn to decompose into a sum w = a1du1 +... +akduk, where the function a l are positive and the ul convex (or quasi-convex) near the origin.
"A convex Darboux Theorem." Methods Appl. Anal. 9 (3) 329 - 344, September 2002.