2 problems

Let $n$ be a positive integer, and consider the $n$-dimensional ball as a domain in $\mathbb{R}^n$. Polterovich–Sher's conjecture. The $n$-dimensional ball is uniquely determined b…

Let $(\Omega,g_1)$ and $(\Omega,g_2)$ be Riemannian surfaces. Two such surfaces are $\sigma$-isometric when their metrics are conformally equivalent, $g_2=\rho g_1$, with…