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Hollow vortices and minimal surfaces

Abstract : 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.
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Martin Traizet. Hollow vortices and minimal surfaces. Journal of Mathematical Physics, American Institute of Physics (AIP), 2015, 56, pp.083101. ⟨10.1063/1.4927248⟩. ⟨hal-01270166⟩

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