Lin-Lin Sun

Counterexamples to Wang's Conjecture

In this paper, we give a negative answer to Wang's conjecture. For every $n\geq 3$, there exist $\varepsilon>0$ and $\delta \in (0,1)$ such that, for all $q$ and $\lambda$ satisfying \[ \frac{n}{n-2}-\varepsilon<q\le \frac{n}{n-2}, \qquad \frac{1}{q-1}\cdot \delta<\lambda\le \frac{1}{q-1}, \] there exists a bounded Euc...