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Let $B_1$ and $B_2$ be two balls in $\mathbb{R}^n$ in $\ell_1$ norm, with distance $d$ and radius $R$. Is there a lower bound on the volume of the intersection between the two n-balls? (assuming the ...

Let $M$ and $N$ be manifolds and let $T: M \to N$ be a bijective map. Let $ \mathcal{F}(M,\mathbb{R})$ (resp.$ \mathcal{F}(N,\mathbb{R})$) be the space of all functions from $M$ (resp. $N$) to $\...

Let $M$ and $N$ be smooth manifolds and $T: M \to N$ be a smooth map. Let $ \mathcal{F}(M,\mathbb{R})$ (resp.$ \mathcal{F}(N,\mathbb{R})$) denote the space of smooth functions from $M$ (resp. $N$) ...

Edit: This question has been significantly revised. Some recent developments in computational geometry (for example see http://geometry.stanford.edu//papers/fmfrmbs-obsbg-12/fmfrmbs-obsbg-12.pdf) ...