3 problems

Let two flat surfaces be equipped with their Steklov spectra. Flat inverse Steklov spectral conjecture. Two flat surfaces are Steklov isospectral if and only if they are isometric.…

Characterization conjecture. A hexagonally triangulated flat plane is conformal to the regular one if and only if the PL conformal factor $w$ is linear.

Let $K$ be a compact nonpositively curved triangle-square complex, let $\widetilde K$ be its universal cover, and let $F$ be an intrinsically aperiodic flat. Intrinsically aperiodi…