OAI/MeasureTheory/Falconer/Angular/MixedCapBounds.lean

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Mixed ambient derivatives of the actual cap bumps

The fixed compactly supported bump is rescaled by an affine similarity. This proves a bound for its full Fréchet derivative, not only the derivative along one selected chart curve. No new regularity assumption is used.

  1. def OAI.Falconer.mixedUnitCapBump line 20
  2. theorem OAI.Falconer.capBump_eq_mixedUnit line 26
  3. theorem OAI.Falconer.iteratedFDeriv_affine_scale_bound line 33
  4. theorem OAI.Falconer.capBump_ambient_derivatives line 58
  5. theorem OAI.Falconer.capBump_ambient_derivative_zero line 81