OAI/GroupTheory/PolycyclicRecognition/Analysis/RegularWalkHarmonic.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

A nonconstant linear-growth harmonic function under polynomial growth

The regular lazy walk has polynomially bounded-below energy. Energy descent therefore supplies normalized coboundaries with vanishing harmonic defect. Scalar projection and pointwise compactness complete the construction.

  1. theorem OAI.PolycyclicRecognition.regularLazyWalk_small_laplacian line 19
  2. theorem OAI.PolycyclicRecognition.polynomial_growth_nonconstant_harmonic line 58
  3. theorem OAI.PolycyclicRecognition.polynomial_growth_harmonic_representation_infinite line 76