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Hausdorff dimension of unions of kk‐planes | Synapse

January 24, 2026Open Access

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Hausdorff dimension of unions of kk‐planes

SGShengwen GanUniversity of Wisconsin–Madison

Puntos clave

This research investigates the Hausdorff dimension of unions of k-planes based on a conjecture by R. Oberlin and Héra.
Proves a conjecture involving unions of k-planes
Applies the Brascamp–Lieb inequality
Utilizes a recent idea developed by Zahl
Establishes the dimension formula under certain conditions
Confirms that the dimension behaves predictably based on the relationship between k and n

Resumen

Abstract We prove a conjecture of R. Oberlin and Héra on the dimension of unions of ‐planes. Let be integers, and . If , with , then . The proof combines a recent idea of Zahl and the Brascamp–Lieb inequality.

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Cite This Study

Shengwen Gan (Thu,) studied this question.

synapsesocial.com/papers/69746090bb9d90c67120a679 https://doi.org/https://doi.org/10.1112/mtk.70071