# A Note on Generic Transversality of Euclidean Submanifolds

@article{Li2018ANO,
title={A Note on Generic Transversality of Euclidean Submanifolds},
author={Siran Li},
journal={manuscripta mathematica},
year={2018},
volume={162},
pages={213-219}
}
• Siran Li
• Published 3 November 2018
• Mathematics
• manuscripta mathematica
In this short note, we establish a quantitative description of the genericity of transversality of $C^1$-submanifolds in $\mathbb{R}^n$: Let $\Sigma \subset \mathbb{R}^n$ be a $d$-dimensional $C^1$-embedded submanifold where $n \geq d+1$. Denote by $$\mathscr{A}(\Sigma) := \bigg\{ a \in \mathbb{R}^n: {\rm volume}\,\Big\{ p\in\Sigma : \partial\mathbb{B}(a, |a-p|) \text{ is not transversal to \Sigma at p} \Big\} > 0 \bigg\}.$$ Then $\mathscr{A}(\Sigma)$ is…
1 Citations
• Mathematics
• 2023
The present paper studies a quantitative version of the transversality theorem. More precisely, given a continuous function f ∈ C ([0 , 1] d , R m ) and a manifold W ⊂ R m of dimension p , a

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