Rigidity of spherical symmetrisation perimeter inequality holds iff the set of radii with cap angle strictly between 0 and π is one interval and the angle is locally W^{1,1} there.
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Rigidity for perimeter inequality under spherical symmetrisation
Rigidity of spherical symmetrisation perimeter inequality holds iff the set of radii with cap angle strictly between 0 and π is one interval and the angle is locally W^{1,1} there.