arXiv subjects

P. N. Ivanshin

Publications and source records attributed to P. N. Ivanshin.

3 recordsLinked to original sources

arXiv2007

Local Lipschitz property of the map which puts in correspondence to N--net its Chebyshev center

We prove local Lipschitz property of the map which puts in correspondence to each $N$--net different from $(N-1)$--net its Chebyshev center. If dimension of Eucledean or Lobachevskii space is greater than 1 and net consists of more than 2 points we show that this map is not Lipschits in a neighbourhood of the space of 2--nets embedded into the space of all $N$--nets endowed by Hausdorff metric.

math.MG↗

arXiv2004

Existence of the Ehresmann connection on a manifold foliated by the locally free action of a commutative Lie group

In this paper the author determines necessary and sufficient conditions for existence of the Ehresmann connection on a manifold foliated by locally free action of the commutative Lie group. Also here we describe structure of $C_0(M)|_L$ for a leaf $L \subset M$ in case such a connection exists. Finally we give some results on structure of the spectrum of the family of Schrödinger operators related to the leaves of the foliation.

math.DG↗

arXiv2004

A Lipschitz map $f: \mathcal{C} \to H$ for the Hadamard space $H$. Sketch of the construction

We introduce the sketch of construction of a Lipschitz function $f: \mathcal{C} \to H$, here the set $\mathcal{C}$ consists of all compact convex subsets of the Hadamard space $H$. Note that $f(\{x\})=\{x\}$ for any point $x \in H$.

math.MG↗