3 problems

Curvature continuity conjecture. The PN-modified Catmull-Clark subdivision can generate curvature-continuous subdivision surfaces, and the extraordinary points of the resulting sur…

Fixed-ratio density conjecture. For every $v\in(0,1)$,

Compactness conjecture for minimizing sequences. There is a sequence of Möbius transformations $G_j$ of $\mathbb{R}^3$ such that the surfaces $G_j\circ\mathbf{x}_j(K)$ can be parti…