We present the first results of our deep survey of lensing clusters aimed at constraining the abundance of star-forming galaxies at z \sim 6 - 10 , using lensing magnification to improve the search efficiency and subsequent spectroscopic studies .
Deep near-IR photometry of two lensing clusters ( A1835 and AC114 ) was obtained with ISAAC/VLT .
These images , combined with existing data in the optical bands including HST images , were used to select very high redshift candidates at z \gtrsim 6 among the optical-dropouts .
Photometric selection criteria have been defined based on the well-proven dropout technique , specifically tuned to target star-forming galaxies in this redshift domain .

We have identified 18 ( 8 ) first and second-category optical dropouts in A1835 ( AC114 ) , detected in more than one filter up to H ( Vega ) \sim 23.8 ( AB \sim 25.2 , uncorrected for lensing ) .
Among them , 8 ( 5 ) exhibit homogeneous SEDs compatible with star-forming galaxies at z \gtrsim 6 , and 5 ( 1 ) are more likely intermediate-redshift EROs based on luminosity considerations .
We have also identified a number of fainter sources in these fields fulfilling our photometric selection and located around the critical lines .
We use all these data to make a first attempt at constraining the density of star-forming galaxies present at 6 \lesssim z \lesssim 10 using lensing clusters .
Magnification effects and sample incompleteness are addressed through a careful modeling of the lensing clusters .
A correction was also introduced to account for the expected fraction of false-positive detections among this photometric sample .

It appears that the number of candidates found in these lensing fields , corrected for magnification , incompleteness and false-positive detections , is higher than the one achieved in blank fields with similar photometric depth in the near-IR .
The luminosity function derived for z \gtrsim 6 candidates appears compatible with that of LBGs at z \simeq 3 , without any renormalization .
The turnover observed by Bouwens et al .
( 2005 ) towards the bright end relative to the z \sim 3 LF is not observed in this sample .
Also the upper limit for the UV SFR density at z \sim 6 - 10 , integrated down to L _ { 1500 } = 0.3 L ^ { * } _ { z = 3 } , of \rho _ { \star } = 7.4 10 ^ { -2 } M _ { \odot } yr ^ { -1 } Mpc ^ { -3 } is compatible with the usual values derived at z \simeq 5 - 6 , but higher than the estimates obtained in the NICMOS Ultra Deep Field ( UDF ) .
The same holds for the upper limit of the SFR density in the z \simeq 8 - 10 interval ( \rho _ { \star } = 1.1 10 ^ { -1 } ) .
This systematic trend towards the bright end of the LF with respect to blank fields could be due to field-to-field variance , a positive magnification bias from intermediate-redshift EROs , and/or residual contamination .
Given the low S/N ratio of the high- z candidates , and the large correction factors applied to this sample , increasing the number of blank and lensing fields with ultra-deep near-IR photometry is essential to obtain more accurate constraints on the abundance of z \gtrsim 6 galaxies .