Densities for Hausdorff measure and rectifiability. Besicovitch’s 1/2-conjecture

Authors

  • Jaume Capdevila Jové Universitat Autònoma de Barcelona

Keywords:

geometric measure theory, Hausdorff measure, rectifiability, Besicovitch’s 1/2-conjecture

Abstract

In this work, we study one of the central concepts of geometric measure theory, that of rectifiable sets, and its relationship with the densities for the Hausdorff measure. Within this interaction lies one of the oldest open problems in the theory: Besicovitch's 1/2-conjecture. We review a selection of relevant results, from Besicovitch’s pioneering papers (1938) to the refinement by Preiss and Tišer (1988). Afterwards, we present an original contribution: we generalize to Rn an example originally given by Besicovitch in the plane, proving its key properties and thus extending a lower bound of the conjecture to arbitrary dimension.

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Published

2025-12-04

How to Cite

Capdevila Jové, J. (2025). Densities for Hausdorff measure and rectifiability. Besicovitch’s 1/2-conjecture. Reports@SCM, 10(1), 77–78. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/156044

Issue

Vol. 10 No. 1 (2025)

Section

Extended abstracts

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