3 problems

Let $\Omega\subset\mathbb{R}^{N+1}$ be a bounded region whose boundary is homeomorphic to the unit sphere in $\mathbb{R}^{N+1}$. Williams conjecture. If $\partial\Omega$ is homeomo…

Ramm's complex exponential Pompeiu conjecture. Under these assumptions, the displayed equation holds for all $\lambda\in\mathbb{R}$ and all $\theta\in[0,2\pi)$ if and only if $D$ i…

Let $D\subset\mathbb{R}^n$ be a bounded domain whose closure is diffeomorphic to a closed ball, with connected $C^1$ boundary $S$. Say that $D$ fails the $P$-property if there exis…