Hollow vortices and minimal surfaces

Martin Traizet (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We consider an overdetermined elliptic problem known as the hollow vortex problem. We prove that the solutions to this problem are in 1:1 correspondence with minimal graphs bounded by horizontal symmetry lines. We use this correspondence to give various examples of domains with hollow vortices.

Domaines: Géométrie différentielle [math.DG]

Martin Traizet. Hollow vortices and minimal surfaces. Journal of Mathematical Physics, 2015, 56, pp.083101. ⟨10.1063/1.4927248⟩. ⟨hal-01270166⟩