Minas Tirith isn't the only place they are battling.
In the book (and extended editions), when Aragorn, Legolas and Gimli exit the Dimholt (with the army of the dead), they find themselves in Southern Gondor, watching Corsairs of Umbar fighting against the armies of Southern Gondor. After the dead help defeat the Corsairs of Umbar, they load the ships up with all the southern soldiers and go to Minas Tirith.
The film also does a poor job of depicting the many soldiers, including the Knights of Dol Amroth, that came to Minas Tirith to defend the city.
It feels good to answer a question like this.. been a while. too bad the boards are going.
The New World fell not to a sword but to a meme.