2 problems

0 votes0 replies1 view
Conjecture on densest prism-group ball arrangements in Nil geometry
Let $\boldsymbol{Nil}$ denote Nil geometry, and let $Gamma_p(q)=\mathbf{pq2_1}$ be the associated isometry group for parameters $(p,q)=(4,4),(3,6),(6,3)$ . Let $\mathcal{B}_p(q)$ be…
Conjecturesolvednil-geometry sphere-packingsarXiv posted 2 days ago
0 votes0 replies0 views
Nonexistence of quadratic-area-growth entire minimal graphs in Nil $_3$
Let Nil $_3$ denote the Heisenberg space, and call a surface an entire minimal graph if it is a minimal graph over the whole horizontal base. A surface has quadratic area growth if…
Conjectureopenarea-growth minimal-surfaces nil-geometryarXiv posted 2 days ago

Conjecture on densest prism-group ball arrangements in Nil geometry