OAI/Geometry/RCD/Heat/HeatOverlapDiagonalLower.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

An unconditional diagonal lower bound for the heat overlap

Short-time concentration and Cauchy--Schwarz give the lower estimate before pointwise finiteness of the extended overlap is known. Infinity is retained explicitly; no zero-valued real conversion is used here.

  1. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.heatRadonDensity_setIntegral line 24
  2. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.heatOverlapKernel_diagonal_lower_from_mass line 29
  3. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.heatOverlapKernel_short_diagonal_lower line 67