OAI/Geometry/RCD/Sobolev/LocalGradientBoundedness.lean

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2 declarations, 0 contain sorry, 0 declared as axioms

Local amplitude bounds from the actual weak gradient

Local transport and differentiation supply Lipschitz representatives. A finite cover then bounds the original Sobolev function on each compact interior ball, without assuming an amplitude bound.

  1. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.local_sobolev_lipschitz line 21
  2. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.local_amplitude_of_gradient line 40