Convexity properties for complements of analytic sets and their amoebas

Images on the Reinhardt diagram for subsets of the complex space plays important role in the complex analysis. For analytic subset images, it is convenient to consider the diagram in the logarithmic scale; in this case, the image is called the amoeba of the analytic set. In the talk, we prove that the well-known $k$-pseudoconvexity property for the complement of the analytic set corresponds to the Gromov-Lefshets $k$-convexity for the amoeba complement.