π_B in asymetric Minkowski normed spaces

2025/10/27 by Múzquiz, Gorka Guardiola
Mathematics · #52 #Advanced Banach Space Theory #Analytic and geometric function theory #FOS: Mathematics #General Mathematics (math.GM) #Point processes and geometric inequalities

paper · doi:10.48550/arxiv.2511.05521

openalex publication_date 2025/10/27 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

We extend the classical results of Stanislaw Golab, on the values of pi in arbitrary normed planes, to asymmetric norms where the unit ball has one axis of symmetry. First, we characterize the values of π_B for different families of polygons as unit ball B. Then we prove that π_B ≥ 3, and can take all possible values and is not bounded in such spaces.

Citations

• Extremal Values of Pi

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