Isoperimetric Inequalities and Amenability
Let (V, g), (W, h) be oriented Riemannian manifolds. A mapping f : V → W is called quasiregular if it is locally Lipschitz, thus differentiable almost everywhere, and if its differential Dfx and Jacobian J(x) satisfy the inequality 0 < ‖Dfx‖n ≤ cJ(x) for almost all x, where c is a constant.
KeywordsRiemannian Manifold Fundamental Group Heisenberg Group Compact Manifold Isoperimetric Inequality
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