7 problems

Let ${\cal M}$ be a polyhedron, let ${\cal D}_l({\cal M})$ be an island of its Stereographic Map labeled by $l$, and let ${\cal A}({\cal D}_l({\cal M}))$ denote the island's area.…

Let ${\cal S}({\cal M})$ be the Stereographic Map of a generic surface ${\cal M}$, decomposed into a countable disjoint union of open sets ${\cal D}_l({\cal M})$, called islands an…

A triply periodic smooth function in ${\mathbb R}^3$ determines a fractal Stereographic Map, a subset of ${\mathbb R}\text{P}^2$. Novikov's conjecture. The Hausdorff dimension of s…

Let $u$ be the total field and let $\tilde{u}$ be the solution of the problem truncated by a perfectly matched layer (PML) in the physical domain $\Omega_H$. Let $\tilde{P}$ denote…

Let the minimizers of the variational problem in the paper be periodic nonlocal-CMC surfaces, with the volume serving as the constraint. Straight cylinders are the configurations d…

Local exponential convergence conjecture. Exponential convergence of the PML method should hold locally also for nonflat periodic surfaces.

Let $\Sigma$ be a surface in the cube tessellation, and let $T^n$ be the quotient torus formed from the tessellation. Call cubes of edge length $2$ large cubes. Assume that each of…