Salle 2
le 22 février 2013 à 10:45
\section{Total curvature} Let
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. \section{Simple Harnack curves} 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. \section{Total Curvature of the Real Amoeba} 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. \section{Total curvature of tropical hypersurfaces} If time , I will quote a recent result about total curvature of Real tropical hypersurfaces.