A local systolic inequality and Gromov's filling area conjecture

2020/09/07 by Olaf Müller, Müller, Olaf
Mathematics · #53C23 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2009.03172

openalex publication_date 2020/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The article treats some questions around Gromov's filling area conjecture. It intended to show that any filling with volume < 2 π would not be attained and to show a local systolic inequality, implying an a priori lower estimate on the total volume. The proof of both assertions, the second of which is wrong, suffered from a computational mistake.

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