OAI/Analysis/RCDHeat/InnerPath.lean

GitHub source file

19 declarations, 0 contain sorry, 0 declared as axioms

Cheeger energy, curvature-dimension transport and heat-flow estimates: InnerPath, HeatHopfPair, HeatHopfActual, HeatKuwada.

  1. theorem OAI.RegularPointCoordinates.inner_lipschitzOn line 17
  2. theorem OAI.RegularPointCoordinates.lipschitzOn_inner_of_lipschitzOn line 40
  3. theorem OAI.RegularPointCoordinates.sub_le_integral_of_ae_deriv_le line 51
  4. theorem OAI.RegularPointCoordinates.SobolevSpace.ofLipschitzCompact_energy_le line 68
  5. theorem OAI.RegularPointCoordinates.heatShift_hasDerivAt line 96
  6. theorem OAI.RegularPointCoordinates.heatShift_lipschitzOn line 101
  7. theorem OAI.RegularPointCoordinates.hj_inner_bound line 113
  8. theorem OAI.RegularPointCoordinates.heat_hj_pair_bound line 141
  9. theorem OAI.RegularPointCoordinates.hopfPathSobolev_energy_le line 160
  10. theorem OAI.RegularPointCoordinates.heat_hopf_regularized_pair line 173
  11. theorem OAI.RegularPointCoordinates.heat_hopf_entropy_pair line 217
  12. theorem OAI.RegularPointCoordinates.hopfLax_hasCompactSupport line 250
  13. theorem OAI.RegularPointCoordinates.hopfLax_integrable_mul line 254
  14. theorem OAI.RegularPointCoordinates.inner_hopfPathSobolev line 258
  15. theorem OAI.RegularPointCoordinates.heat_hopf_entropy_dual line 268
  16. theorem OAI.RegularPointCoordinates.transportCost_le_of_scaled line 337
  17. theorem OAI.RegularPointCoordinates.integral_heatMeasure line 355
  18. theorem OAI.RegularPointCoordinates.heat_coupling_entropy line 365
  19. theorem OAI.RegularPointCoordinates.heat_coupling_fisher_action line 394