5 problems

Fractal flat surface conjecture. There exists a surface $\mathcal{S}(KS)$ that can be appropriately viewed as a suitable limit of the flat surfaces $\mathcal{S}(KS_n)$ and such tha…

Veech dichotomy conjecture. Under this assumption, the Veech dichotomy will hold for the Koch snowflake billiard table $\Omega(KS)$.

Infinite-genus fractal flat surface conjecture. The surface $\mathcal{S}(KS)$ is a well-defined flat surface of infinite genus, has a fractal, self-similar structure, and has geode…

Self-similar geometry conjecture. The self-similarity of the Koch snowflake curve is somehow reflected in the geometry of $\mathcal{S}(KS)$.

Footprint conjecture. If $x_0^0\in I$ and $\{\mathscr{O}_i(x_i^0,\pi/3)\}_{i=0}^\infty$ is a compatible sequence of generalized piecewise Fagnano orbits, then there exists a suitab…