Evolution by Levi form in \(\mathbb{P}^2\) (Q2075660)

Summary: In this paper we introduce the notion of evolution by Levi form of a closed set \(K\) in the complex projective space \(\mathbb{P}^2\), which is governed by a parabolic problem for the Levi operator. The main result of the paper is the following: if \(K\) is the closure of a pseudoconvex domain with a regular boundary then the evolution is contained in \(K\). As a consequence, a hypothetic Levi flat hypersurface in \(\mathbb{P}^2\) would be left fixed by evolution.