OAI/Analysis/CircleDomains/Topology/CircleComponentCoordinates.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

Center and radius coordinates of circle-domain components

If a circle domain contains infinity, every complementary component is an ordinary closed disk, allowing radius zero. A bound on the whole complement bounds both parameters. Thus no choice of disk coordinates is an extra hypothesis in the marked-disk compactness argument.

  1. theorem OAI.CircleDomainRigidity.circleDomain_component_eq_closedBall line 20
  2. theorem OAI.CircleDomainRigidity.closedBall_parameters_bound line 40
  3. theorem OAI.CircleDomainRigidity.bounded_circleDomain_component_parameters line 62