Resolving the base of the relativistic jet in M87 at 6$R_{\rm sch}$
  resolution with global mm-VLBI
  M87 is one of the nearest radio galaxies with a central SMBH and a prominent
relativistic jet. Due to its close distance to the observer and the large SMBH
mass, the source is one of the best laboratories to obtain strong observational
constraints on the theoretical models for the formation and evolution of the
AGN jets. In this article, we present preliminary results from our ongoing
observational study about the innermost jet of M87 at an ultra-high resolution
of $\sim$50${\mu}$as achieved by the Global Millimeter-VLBI Array (GMVA). The
data obtained between 2004 and 2015 clearly show limb-brightened jets at
extreme resolution and sensitivity. Our preliminary analysis reveals that the
innermost jet expands in an edge-brightened cone structure (parabolic shape)
but with the jet expansion profile slightly different from the outer regions of
the jet. Brightness temperatures of the VLBI core obtained from cm- to
mm-wavelengths show a systematic evolution, which can be interpreted as the
evolution as a function of distance from the BH. We also adopt an alternative
imaging algorithm, BSMEM, to test reliable imaging at higher angular resolution
than provided by the standard CLEAN method (i.e. super-resolution). A
demonstration with a VLBA 7mm example data set shows consistent results with a
near-in-time 3mm VLBI image. Application of the method to the 2009 GMVA data
yields an image with remarkable fine-scale structures that have been never
imaged before. We present a brief interpretation of the complexity in the
structure.
