In negatively curved 3-manifolds, the marked p-energy spectrum and the modified energy entropy of k-surfaces are rigid: equality or asymptotic behavior forces the ambient curvature to be constant.
Ahlfors.Lectures on quasiconformal mappings
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Rigidity of the hyperbolic marked energy spectrum and entropy for $k$-surfaces
In negatively curved 3-manifolds, the marked p-energy spectrum and the modified energy entropy of k-surfaces are rigid: equality or asymptotic behavior forces the ambient curvature to be constant.