In this paper, we study the extension of the minimizing equal mass parallelogram solutions which was derived by Chen in 2001 . Chen's solution was minimizing for one quarter of the period $[0,T]$, where numerical integration had been used in his proof. In this paper we extend Chen's solution in the reduced space to $[0,4T]$ and we show that this extension is also minimizing over the intervals $[0,2T]$ and $[0,4T]$. The minimizing property of the extension is proved without using numerical integration.
"Extensions to Chen's Minimizing Equal Mass Parallelogram Solutions." Taiwanese J. Math. 21 (6) 1437 - 1453, December, 2017. https://doi.org/10.11650/tjm/171003