On the curvature of the real amoeba

2010/12/30 by Passare, Mikael, Risler, Jean-Jacques
#14Pxx #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1101.0095

Abstract

For a real smooth algebraic curve A ⊂ (\mathhbbC^*)², the amoeba A ⊂ ℝ² is the image of A under the map Log : (x,y) ↦ (log |x|, log | y |). We describe an universal bound for the total curvature of the real amoeba A_{ℝ A} and we prove that this bound is reached if and only if the curve A is a simple Harnack curve in the sense of Mikhalkin.

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