OAI/Geometry/RCD/Transport/RadialGeodesic.lean

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4 declarations, 0 contain sorry, 0 declared as axioms

Radial midpoint rigidity and distance along a minimizing path

The nonnegative quadratic midpoint defect has zero integral for an optimal coupling to a radial midpoint. Its zero set consists precisely of metric midpoints on rays towards the pole.

  1. theorem OAI.RegularPointCoordinates.radial_midpoint_defect_nonneg line 18
  2. theorem OAI.RegularPointCoordinates.radial_midpoint_of_defect_zero line 26
  3. theorem OAI.RegularPointCoordinates.IsGeodesic.radial_distance line 38
  4. theorem OAI.RegularPointCoordinates.IsGeodesic.inwardDistance_increment line 56