9 problems

Möbius uniqueness conjecture. Every edge-scribable $(d+1)$-polytope is Möbius unique.

In the Möbius geometry of the 4-sphere, a Willmore surface is a surface that is critical for the Willmore functional, and its Möbius curvature is the curvature of its conformally i…

Let $Q(k,\theta)$ denote the quotient studied in the paper, with $0<k<1$ and $0<\theta<2\pi$. The sharp quotient bounds conjecture. For all such $k$ and $\theta$, … and … The conje…

The sector cross-ratio supremum conjecture. One has

Identify $\mathbb{R}^4$ with the quaternion skew field $\mathbb{H}$. Let an analytic surface in $\mathbb{R}^4$ have two noncospheric circular arcs through every point, fully contai…

An analytic surface in $\mathbb{R}^3$ is the image of an injective real analytic map from a planar domain with nondegenerate differential at every point. Two circular arcs are tran…

The examples under consideration include Euclidean translational surfaces, Clifford translational surfaces, Darboux cyclides, and their images under Möbius transformations. A surfa…

Buyalo–Schroeder conjecture. Every compact Ptolemy space with properties (E) and (I) is Möbius equivalent to the boundary at infinity of a rank one symmetric space…

Let $n$ and $r$ be the dimensions under consideration, and let $f:\hat{\mathbb{R}}^n\to\hat{\mathbb{R}}^n$ be a map that sends every $r$-dimensional sphere into an $r$-dimensional…