OAI/Analysis/CircleDomains/Sobolev/LocalZeroGradientConstant.lean

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A continuous planar Sobolev function with zero weak gradient on a connected open set is constant there and on its closure. The proved local complex Weyl lemma reduces this to the holomorphic open mapping theorem.

  1. theorem OAI.CircleDomainRigidity.constant_on_closure_of_zero_weak_gradient line 14
  2. theorem OAI.CircleDomainRigidity.constant_on_homeomorphic_disk line 52