OAI/Analysis/CircleDomains/Uniformization/MobiusConformal.lean

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14 declarations, 0 contain sorry, 0 declared as axioms

Holomorphy of the explicit normalizing Möbius maps

The affine chart at infinity is the rational function z / (a + b z). This gives a nonzero derivative there as well as in every finite chart.

  1. theorem OAI.CircleDomainRigidity.finiteCoord_coe line 19
  2. theorem OAI.CircleDomainRigidity.finiteCoord_sphereInv_coe line 21
  3. theorem OAI.CircleDomainRigidity.chart_coe_apply line 25
  4. theorem OAI.CircleDomainRigidity.chart_coe_self line 29
  5. theorem OAI.CircleDomainRigidity.chart_infty_apply line 32
  6. theorem OAI.CircleDomainRigidity.sphereInv_infty line 35
  7. theorem OAI.CircleDomainRigidity.sphereInv_zero line 37
  8. theorem OAI.CircleDomainRigidity.chart_infty_self line 40
  9. theorem OAI.CircleDomainRigidity.chartSymm_coe_apply line 43
  10. theorem OAI.CircleDomainRigidity.affineSphere_coe line 46
  11. theorem OAI.CircleDomainRigidity.affineSphere_infty line 49
  12. theorem OAI.CircleDomainRigidity.isConformalAt_inversion line 52
  13. theorem OAI.CircleDomainRigidity.affine_chart_at_infinity line 86
  14. theorem OAI.CircleDomainRigidity.isConformalAt_affineSphere line 96