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Conformal dimension measures the extent to which the Hausdorff dimension of a metric space can be lowered by quasisymmetric deformations. Introduced by Pansu in
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Two-Dimensional Conformal Geometry and Vertex Operator Algebras
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Non-perturbative Methods in 2 Dimensional Quantum Field Theory
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The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions.