Rigid cantor sets in $R^3$ with simply connected complement

Simply-connected Nonpositive Curved Surfaces in R3

where |B| is the length of second fundamental form. |B|2 = 4|H|2 − 2K, where H is the mean curvature and K is the Gauss curvature. The curvature of minimal surfaces is nonpositive. Then we exam what is still hold for some minimal surface theorems if extending the minimal condition H ≡ 0 to the surfaces with K ≤ 0 and (1). In 2001, F. Xavier [18] has the following theorem: Theorem [Xavier]. Let ...

ALGEBRAS WITH CYCLE-FINITE STRONGLY SIMPLY CONNECTED GALOIS COVERINGS

Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...

Cantor sets

This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space ω of irrationals, or certain of its subspaces. In particular, given f ∈ (ω\{0}), we consider compact sets of the form Q i∈ω Bi, where |Bi| = f(i) for all, or for infinitely many, i. We also consider “n-splitting” compact sets, i.e., compact sets K such that for any f ∈ K and i ∈ ω, |{g(i) : ...

Cantor Sets with Complicated Geometryand

A Cantor Set with Hyperbolic Complement

We construct a Cantor set in S3 whose complement admits a complete hyperbolic metric.