All Questions
Tagged with packing-and-covering smooth-manifolds
4 questions
6
votes
1
answer
310
views
Asymptotic bound on minimum epsilon cover of arbitrary manifolds
Let $M \subset \mathbb{R}^d$ be a compact smooth $k$-dimensional manifold embedded in $\mathbb{R}^d$. Let $\mathcal{N}(\varepsilon)$ denote the minimal cardinal of an $\varepsilon$-cover $P$ of $M$; ...
- 71
1
vote
0
answers
123
views
Subdividing a Compact Bounded Curvature Manifold into Charts with Bounded Lipschitz Constant
Let $M \subset \mathbb{R}^d$ be a compact smooth $k$-dimensional manifold embedded in $\mathbb{R}^d$. Let $\mathcal{N}(\epsilon)$ denote the size of the minimum $\epsilon$ cover $P$ of $M$; that is ...
- 71
1
vote
0
answers
103
views
Upper bounds on $\epsilon$-covers of arbitrary compact manifolds
Let $M \subset \mathbb{R}^d$ be a compact $k$-dimensional manifold embedded in $\mathbb{R}^d$. Let $\mathcal{N}(\epsilon)$ denote the size of the minimum $\epsilon$-cover $P$ of $M$, that is for every ...
- 71
4
votes
0
answers
134
views
Lower bound on $\epsilon$-covers of arbitrary manifolds
Let $M \subset \mathbb{R}^d$ be a $k$-dimensional manifold embedded in $\mathbb{R}^d$. Let $\mathcal{N}(\epsilon)$ denote the size of the minimum $\epsilon$-cover $P$ of $M$, that is for every point $...
- 71