Normalized conservative statistical structures on closed orientable surfaces of genus at least 2 are completely parameterized by a holomorphic vector bundle over Teichmüller space consisting of Abelian differentials and cubic differentials.
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On Conservative Statistical Riemann Surfaces
Normalized conservative statistical structures on closed orientable surfaces of genus at least 2 are completely parameterized by a holomorphic vector bundle over Teichmüller space consisting of Abelian differentials and cubic differentials.