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A holomorphic motion with non-subharmonic Hausdorff dimension

Year: 2026

Type: preprint

Abstract: We present an example of a holomorphic motion of a Cantor set $λ\mapsto A_λ$ for which neither the Hausdorff dimension $\dimH(A_λ)$ nor the lower Minkowski dimension $\dimMl(A_λ)$ is a subharmonic function of~$λ$. This answers negatively a question of Fuhrer--Ransford--Younsi, and distinguishes these dimensions from packing and upper Minkowski dimensions, for which subharmonicity holds. All four dimensions are computed explicitly.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.22644

Authors: Ransford, Thomas, Younsi, Malik

Institutions: University of Hawaiʻi at Mānoa, University of Hawaii System, Université Laval

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Natural Sciences and Engineering Research Council of Canada

Awards: G1119843451, Removability in Geometric Function Theory

OpenAlex ID: W7222924607

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