2 problems

Let $X\subset \mathbb{C}^n$ and $Y\subset \mathbb{C}^m$ be complex analytic sets with $\dim X=\dim Y=d$. Their germs at zero are bi-Lipschitz homeomorphic if there is a bi-Lipschit…

Local uniform Sobolev inequality conjecture. There exist a neighbourhood $U$ of $o$ in $N$ and a constant $C$, independent of $\delta$, such that every positive $\mathcal C^1$ func…