OAI/Geometry/RCD/Heat/CanonicalHeatKernel.lean

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8 declarations, 0 contain sorry, 0 declared as axioms

The canonical symmetric heat-kernel candidate

The half-time overlap fixes one symmetric representative at all points, with measurability, mass conservation and semigroup representation. Continuity and finiteness of the underlying extended overlap are not presumed.

  1. def OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalHeatKernel line 23
  2. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalHeatKernel_nonneg line 27
  3. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalHeatKernel_symmetric line 33
  4. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalHeatKernel_measurable line 40
  5. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalHeatKernel_ae line 48
  6. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalHeatKernel_integrable line 57
  7. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalHeatKernel_mass_one line 61
  8. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalHeatKernel_represents line 66