4 problems

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…

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…