A new bounded cochain extension operator for differential forms on Lipschitz domains achieves global commutativity with the exterior derivative on the complement of harmonic forms and yields uniform Poincaré inequalities plus Neumann eigenvalue bounds on non-convex domains.
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Uniformly Bounded Cochain Extensions and Uniform Poincar\'e Inequalities
A new bounded cochain extension operator for differential forms on Lipschitz domains achieves global commutativity with the exterior derivative on the complement of harmonic forms and yields uniform Poincaré inequalities plus Neumann eigenvalue bounds on non-convex domains.