2 problems

Let ${{\mathbb C}}o^2=\\{(\xi_1,\xi_2,\sqrt{\xi_1^2+\xi_2^2}):1\leq \xi_1^2+\xi_2^2\leq 2\\}$ be the truncated cone, and let $\Gamma(\delta)$ partition its $\delta$-neighborhood in…

Let ${\mathcal C}^2=\{(\xi_1,\xi_2,\sqrt{\xi_1^2+\xi_2^2}):\frac14\leq\xi_1^2+\xi_2^2\leq4\}$, and let ${\mathcal N}_\delta({\mathcal C}^2)$ denote its $\delta$-neighborhood. Suppo…