OAI/Analysis/CircleDomains/Topology/UnorientedCircleGreen.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

The orientation-independent form of the same published Green input.

M. Spivak, Calculus on Manifolds (1965), Theorem 5-5, p.124. A regular once-traversed Jordan boundary has one of the two orientations; the sign below changes its integral to the positive boundary orientation. Inner circles retain their positive disk orientation. This is the signed parametrized specialization of the same manifold Stokes theorem cited in FiniteCircleGreen.lean, not an energy or uniformization assumption. The sign is chosen before the holes and the differential form.

  1. def OAI.CircleDomainRigidity.UnorientedFiniteCircleGreenFormula line 23
  2. theorem OAI.CircleDomainRigidity.finiteCircleGreen_regular_weighted_closed_form line 38
  3. theorem OAI.CircleDomainRigidity.finite_circle_stokes_area_bound_regular line 73