2019/02/25 by Erika Pieroni, Pieroni, Erika · 2 citations
Mathematics · #53C20 #57M50 #57N16 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1902.09190
openalex publication_date 2019/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compute the Minimal Entropy of every closed, orientable 3-manifold, showing that its cube equals the sum of the cubes of the minimal entropies of each hyperbolic component arising from the JSJ decomposition of each prime summand. As a consequence we show that the cube of the Minimal Entropy is additive with respect to both the prime and the JSJ decomposition, thus concluding that for closed orientable 3-manifolds the cube of the Minimal Entropy is proportional to the simplicity volume. This answers a conjecture asked by Anderson and Paternain for irreducible manifolds.