OAI/Geometry/RCD/Heat/CanonicalL2Rows.lean

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8 declarations, 0 contain sorry, 0 declared as axioms

Continuity of the canonical heat kernel through L² rows

Local kernel bounds and uniform square-integrable tails follow from the actual RCD heat flow. Quantitative L¹ continuity then implies L² continuity, and the half-time overlap is a continuous inner product.

  1. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalHeatKernel_ae_radon line 25
  2. def OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalL2Row line 30
  3. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalL2Row_coe line 35
  4. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalL2Row_integrable line 40
  5. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalL2Row_continuous line 46
  6. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalHeatKernel_eq_inner line 112
  7. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalHeatKernel_continuous_joint line 143
  8. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.canonicalHeatKernel_continuous_right line 150