OAI/MeasureTheory/Falconer/Geometry/ChartFrame.lean

GitHub source file

4 declarations, 0 contain sorry, 0 declared as axioms

Choosing a frame adapted to a failed perpendicular test

Two Householder reflections map a fixed orthonormal pair to a prescribed one. This places the nonstationary tangent direction in the first chart coordinate without any loss depending on the cap center.

  1. theorem OAI.Falconer.orthonormal_pair_isometry line 17
  2. theorem OAI.Falconer.exists_adapted_chart_frame line 35
  3. theorem OAI.Falconer.inner_isometry_pullback line 41
  4. theorem OAI.Falconer.normalizedLine_isometry line 45