8 problems

Let $B$ be a perfectly reflecting, possibly disconnected, closed bounded body in Euclidean space. An oriented ray is a ray of invisibility with $k$ reflections if, after finitely m…

Convex refractor existence conjecture. Under these hypotheses, such a convex weak solution exists for the target set and data described above.

Interpolated-reflector existence conjecture. There exists an interpolated reflector $R\in \mathcal{R}_2^{\mathscr{C}_U^\delta(z')}(T)$ such that $G_2(\{x_i\})=f_i$ for every…

Generalized-reflector existence conjecture. There exists a generalized reflector $R\in \mathcal{R}_1^{\mathscr{C}_U^\delta(z')}(T)$ such that $G_1(\{x_i\})=f_i$ for every…

Nonidentity conjecture for reflection compositions. No well-defined composition of reflections from smooth germs of hypersurfaces can be equal to the identity.

Let $Q$ be an open subset of $\mathbb{R} \times \overline{\Omega}$, where $\Omega$ is the spatial domain, and let $T$ be an observation time. A generalized bicharacteristic is a ge…

Billiard invisibility conjecture. (a) Given a finite set of directions and a finite set of points, there is a body invisible in these directions and from these points. (b) The set…

Let $M_n$ be sets of mirrors and let $\Lambda$ denote the measure on light rays. The sets $M_n$ are required to satisfy the conclusions of Theorem 16.2 except condition (b), namely…