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arXiv · 2607.15500

H\"older functions with nonporous graphs

Claudio A. DiMarco
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Abstract

For any $\alpha \in (0,1)$ there is a H\"older continuous function $h:\mathbb{R} \rightarrow \mathbb{R}$ with nonporous graph $Gr(h) \subset \mathbb{R}^2$ which is thin for doubling measures. Construction of these functions requires analysis of a known example with nonporous graph and bounded variation on the unit interval.

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Claudio A. DiMarco. 2026-07-16. H\"older functions with nonporous graphs. https://arxiv.org/abs/2607.15500

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