  Based on MUSE integral-field data we present evidence for a radial variation
at the low-mass end of the stellar initial-mass function (IMF) in the central
regions of the giant early-type galaxy NGC4486 (M87). We used state-of-the-art
stellar population models and the observed strength of various IMF-sensitive
absorption-line features to solve for the best low-mass tapered "bimodal" form
of the IMF, while accounting also for radial variations in stellar metallicity,
the overall $\alpha$-elements abundance, and the abundance of individual
elements such as Ti, O, Na and Ca. Our analysis reveals a strong IMF gradient
in M87, corresponding to an exceeding fraction of low-mass stars compared to
the case of the Milky Way toward the center of M87 that drops to nearly
Milky-way levels by 0.4 $R_e$. This IMF gradient is found to correlate well
with both the radial profile for stellar metallicity and for $\alpha$-elements
abundance but not with stellar velocity dispersion. Such IMF variations
correspond to over a factor two increase in stellar mass-to-light M/L ratio
compared to the case of a Milky-way like IMF, consistent with other
investigations into IMF gradients in early-type galaxies, including recent
dynamical constraints on M/L radial variations in M87 by Oldham & Auger. In
addition to constraining the IMF in M87 we also looked into the abundance of
Sodium, which turned up to be super-Solar over the entire radial range of our
MUSE observations and to exhibit a considerable negative gradient. These
findings suggest an additional role of metallicity in boosting the Na-yields in
the central, metal-rich regions of M87 during its early and brief
star-formation history. Our work adds the case of M87 to the few objects that
as of today have radial constraints on their IMF or [Na/Fe] abundance, while
also illustrating the accuracy that MUSE could bring to this kind of
investigations.
