Discrete Approximations of Metric Measure Spaces of Controlled Geometry

2014/08/09 by James T. Gill, Gill, James T., Marcos López +1
Mathematics · #30L05 (Primary) 31E05 (Secondary) #FOS: Mathematics #Fixed Point Theorems Analysis #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1408.2132

openalex publication_date 2014/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find a necessary and sufficient condition for a doubling metric space to carry a (1,p)-Poincare inequality. The condition involves discretizations of the metric space and Poincare inequalities on graphs.

Citations

• Brownian Motion and Harmonic Analysis on Sierpinski Carpets
• Inverse limit spaces satisfying a Poincare inequality

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