A Mattila-Sjölin theorem for simplices in low dimensions

In this paper we show that if a compact set \(E \subset \mathbb{R}^d\), \(d \geq 3\), has Hausdorff dimension greater than \(\frac{(4k-1)}{4k}d+\frac{1}{4}\) when \(3 \leq d

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Eyvindur Ari Palsson, Francisco Romero Acosta
Format: Article
Language:English
Subjects:
Apexes
Theorems
Online Access:Get full text
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Summary:In this paper we show that if a compact set \(E \subset \mathbb{R}^d\), \(d \geq 3\), has Hausdorff dimension greater than \(\frac{(4k-1)}{4k}d+\frac{1}{4}\) when \(3 \leq d
ISSN:2331-8422