Spheres are the unique admissible domains for the exterior overdetermined problem with Neumann data proportional to mean curvature when Γ ≥ N-2 among star-shaped domains (and all bounded domains when Γ = N-2) in N ≥ 3, with further results for Γ ≤ 0 and in 2D.
Radial symmetry for elliptic boundary-value problems on exterior domains.Arch
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Proves sharp global rigidity of the unit circle for small Weber numbers in 2D hollow vortex free boundary problem, supporting Crowdy-Wegmann conjecture, plus isoperimetric-isocapacitary inequality and variational classification.
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Spherical rigidity for an exterior overdetermined problem with Neumann data prescribed by mean curvature
Spheres are the unique admissible domains for the exterior overdetermined problem with Neumann data proportional to mean curvature when Γ ≥ N-2 among star-shaped domains (and all bounded domains when Γ = N-2) in N ≥ 3, with further results for Γ ≤ 0 and in 2D.
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Global rigidity of two-dimensional bubbles
Proves sharp global rigidity of the unit circle for small Weber numbers in 2D hollow vortex free boundary problem, supporting Crowdy-Wegmann conjecture, plus isoperimetric-isocapacitary inequality and variational classification.