Context : Some galaxy clusters exhibit shallow or even cored dark matter density profiles in their central regions rather than the predicted steep or cuspy profiles , conflicting with the standard understanding of dark matter .
NGC 3311 is the central cD galaxy of the Hydra I cluster ( Abell 1060 ) .

Aims : We use globular clusters around NGC 3311 , combined with kinematical data of the galaxy itself , to investigate the dark matter distribution in the central region of Hydra I .

Methods : Radial velocities of 118 bright globular clusters , based on VLT/VIMOS mask spectroscopy , are used to calculate velocity dispersions which are well defined out to 100 kpc .
NGC 3311 is the most distant galaxy for which this kind of study has been performed .
We also determine velocity dispersions of the stellar component from long slit spectroscopy of NGC 3311 with VLT/FORS1 out to 20 kpc .
Moreover , we present a new photometric model for NGC 3311 , based on deep VLT/FORS1 images in the V-band .
We search for a dark halo which in the context of a spherical Jeans model can reproduce the kinematical data .
We also compare the radial velocity distributions of globular clusters and planetary nebulae .

Results : The projected stellar velocity dispersion rises from a central low value of about 185 km/s to 350 km/s at a radius of 20 kpc .
The globular cluster dispersion rises as well from 500 km/s at 10 kpc to about 800 km/s at 100 kpc , comparable to the velocity dispersion of the cluster galaxies .
A dark matter halo with a core ( Burkert.halo ) reproduces well the velocity dispersions of stars and globular clusters simultaneously under isotropy .
The central stellar velocity dispersions predicted by cosmological NFW halos are less good representations , while the globular clusters allow a wide range of halo parameters .
A suspected radial anisotropy of the stellar population as found in merger simulations aggravates the deviations .
A slight tangential anisotropy permits better representations .
However , we find discrepancies with previous kinematical data , which we can not resolve and which may indicate a more complicated velocity pattern .

Conclusions : Although one can not conclusively demonstrate that the dark matter halo of NGC 3311 has a core rather than a cusp , a core seems to be preferred by the present data .
A more complete velocity field and an analysis of the anisotropy is required to reach firm conclusions .