6 problems

For positive integers $n$ and $d$, let $b[?m\lambda(n,d)b[?0m$ be the minimal number of vertices of a triangulation $K$ of the $n$-sphere admitting a simplicial map of degree $d$ t…

Let $\mathbb{S}^n$ and $\mathbb{S}^m$ be spheres, and let a map between them be area-decreasing, meaning that its induced action decreases the areas of tangent $2$-planes. Gromov's…

Let $f:S^n\to S^m$ be a smooth map between standard unit spheres, and let the $2$-dilation of $f$ be the supremum of the norms of the induced maps on $2$-dimensional tangent planes…

Let $H:\mathbb{S}^{2n-1}\rightarrow\mathbb{S}^{2N-1}$ be a sphere map with linearly independent components, and let $s>0$. Degree conjecture. If $H$ is $s$-degenerate, then $H$ has…

Guth's conjecture. If $n\geq 4$, then there exists a map $f\in C^1(\mathbb S^{n+1},\mathbb S^n)$ such that

Let $S^n\subset\mathbb{C}^{n+1}$ and $S^N\subset\mathbb{C}^{N+1}$ be unit spheres, and let a CR map between them be $C^2$-smooth and non-constant. The codimension is $N-n$. Cima–Su…