be a smooth algebraic hypersurface. Then the total curvature of is the "volume" of the Gauss map
The total curvature of the real Amoeba is then the volume of the image of
the Logarithmic Gauss map.
I will recall the definition of G. Mikhalkin, and the theorem of Mikhalkin-
Rullgard which characterize plane Simple Harnack curves by the fact that the
Amoeba has maximal area.
I will give a bound for the total curvature of the real Amoeba of a real plane
curve (in term of its Newton Polygon) and prove that this bound is reached
if and only if is a (smooth) simple Harnack curve.
If time , I will quote a recent result about total curvature of Real tropical