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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.09354 |
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Table of Contents:
- Uniformly perfect measures are a common generalisation of Ahlfors regular measures, self-conformal measures on the line, and their push-forwards under sufficiently regular maps. We show that every uniformly perfect measure $σ$ on a strictly convex planar $C^{2}$-graph is $L^{2}$-flattening. That is, for every $ε>0$, there exists $p = p(ε,σ) \geq 1$ such that $$\|\hatσ\|_{L^{p}(B(R))}^{p} \lesssim_{ε,σ} R^ε, \qquad R \geq 1.$$