OAI/Geometry/SurfaceImmersion/Primitive/PositiveAtlasPrimitives.lean

GitHub source file

13 declarations, 0 contain sorry, 0 declared as axioms

The normalized atlas gives an actual finite positive primitive family. The amplitudes are smooth and supported in the original chart supports; their rank-one tensors sum exactly to the given symmetric tensor.

  1. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.positivePrimitiveAmplitude line 35
  2. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.positivePrimitiveTensor line 38
  3. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.positivePrimitiveAmplitude_nonneg line 43
  4. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.positivePrimitiveAmplitude_support line 48
  5. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.positivePrimitiveAmplitude_pos_iff line 53
  6. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.positivePrimitiveAmplitude_tsupport line 69
  7. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.positivePrimitiveTensor_apply line 85
  8. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.positivePrimitiveTensor_symmetric line 105
  9. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.positivePrimitiveTensor_nonneg line 111
  10. theorem OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.sum_positivePrimitiveTensor line 117
  11. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.positivePrimitiveAmplitude_hasCompactSupport line 139
  12. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.positivePrimitiveAmplitude_smooth line 143
  13. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.positivePrimitiveTensor_smooth line 154