OAI/Analysis/CircleDomains/Sobolev/CircleBranchEnergy.lean

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A fixed principal branch is globally bounded, is smooth away from its cut, and has precisely the intrinsic circle differential there. Thus a local branch consumes only the original coordinate's energy.

  1. theorem OAI.CircleDomainRigidity.FiniteTransfer.circleBranch_mem_Ico line 16
  2. theorem OAI.CircleDomainRigidity.FiniteTransfer.circleBranch_abs_le line 19
  3. theorem OAI.CircleDomainRigidity.FiniteTransfer.continuousOn_circleBranch line 26
  4. theorem OAI.CircleDomainRigidity.FiniteTransfer.smooth_circleBranch line 34
  5. theorem OAI.CircleDomainRigidity.FiniteTransfer.fderiv_circleBranch line 42
  6. theorem OAI.CircleDomainRigidity.FiniteTransfer.circleBranch_energy_le line 54