We use the largest sample of z \sim 6 galaxies to date from the first four Hubble Frontier Fields clusters to set constraints on the shape of the z \sim 6 luminosity functions ( LFs ) to fainter than M _ { UV,AB } = -14 mag .
We quantify , for the first time , the impact of magnification uncertainties on LF results and thus provide more realistic constraints than other recent work .
Our simulations reveal that for the highly-magnified sources the systematic uncertainties can become extremely large fainter than - 14 mag , reaching several orders of magnitude at 95 % confidence at \sim - 12 mag .
Our new forward-modeling formalism incorporates the impact of magnification uncertainties into the LF results by exploiting the availability of many independent magnification models for the same cluster .
One public magnification model is used to construct a mock high-redshift galaxy sample that is then analyzed using the other magnification models to construct a LF .
Large systematic errors occur at high magnifications ( \mu \gtrsim 30 ) because of differences between the models .
The volume densities we derive for faint ( \gtrsim - 17 mag ) sources are \sim 3-4 \times lower than one recent report and give a faint-end slope \alpha = -1.92 \pm 0.04 , which is 3.0-3.5 \sigma shallower ( including or not including the size uncertainties , respectively ) .
We introduce a new curvature parameter \delta to model the faint end of the LF and demonstrate that the observations permit ( at 68 % confidence ) a turn-over at z \sim 6 in the range - 15.3 to - 14.2 mag , depending on the assumed lensing model .
The present consideration of magnification errors and new size determinations raise doubts about previous reports regarding the form of the LF at > -14 mag .
We discuss the implications of our turn-over constraints in the context of recent theoretical predictions .