2019
Том 71
№ 11

All Issues

Mirzaie R.

Articles: 2
Article (Ukrainian)

On Typical Compact Submanifolds of the Euclidean Space

Mirzaie R.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 7. - pp. 1009–1014

It is shown that typical compact submanifolds of R n are nowhere differentiable with integer box dimensions.

Brief Communications (English)

On fundamental group of Riemannian manifolds with ommited fractal subsets

Mirzaie R.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 6. - pp. 854-858

We show that if $K$ is a closed and bounded subset of a Riemannian manifold $M$ of dimension $m > 3$, and the fractal dimension of $K$ is less than $m - 3$, then the fundamental groups of $M$ and $M - K$ are isomorphic.