Khavinson, D.; Mineev-Weinstein, M.; Putinar, M.; Teodorescu, R. Lemniscates do not survive Laplace growth. (English) Zbl 1236.30006 Math. Res. Lett. 17, No. 2, 335-341 (2010). The Polubarinova-Galin equation models the movement of the boundary between two fluids in the plane when a sink or source is present. (For background material see [B. Gustafsson and A. Vasil’ev, Conformal and potential analysis in Hele-Shaw cells. Advances in Mathematical Fluid Mechanics. Basel: Birkhäuser (2006; Zbl 1122.76002)].) In the present paper it is shown that the only polynomial lemniscates moving under this process of Laplacian growth (in fact, under a somewhat larger class of processes which are invariant under time reversal) are concentric circles. Reviewer: Hubert Kalf (München) Cited in 1 ReviewCited in 2 Documents MSC: 30C20 Conformal mappings of special domains 35R37 Moving boundary problems for PDEs 76D27 Other free boundary flows; Hele-Shaw flows Keywords:Polubarinova-Galin equation; fluid movement; polynomial lemniscates PDF BibTeX XML Cite \textit{D. Khavinson} et al., Math. Res. Lett. 17, No. 2, 335--341 (2010; Zbl 1236.30006) Full Text: DOI arXiv