Maximal distance minimizers 
For a given compact set M and a number r>0 maximal distance minimizer (MDM) is a connected set of minimal length such that M is contained in the closed r-neighbourhood of it

• • An overview  of maximal distance minimizers: here we  (D. Cherkashin, Y.) wrote all we knew about MDM in 2022 a.d.

  • Regularity of maximal distance minimizers: here we (A. Gordeev, Y.) proved that in Euclidean space  every point of MDM have at most 3 tangent rays and in Euclidean plane the number of points with three tangent rays is finite.

  • We (D. Cherkashin, A. Gordeev, G. Strukov, Y. ) found MDM for a circle (actually not for every circle and not only for circle) and for a rectangle (in this work some computer search was used ).

Steiner trees with infinite number of branching points
Steiner tree is a set of minimal length connecting the giving set of points. Points of Seiner tree have degree at most 3. Points of degree 3 are called branching points.

• • We (E. Paolini, E. Stepanov, Y.) constructed a full Steiner tree with infinite number of branching points.

  • We (D. Cherkashin, Y.) constructed a set of positive Hausdorff dimension such that its Steiner tree has infinite number of branching points.

  • We (D. Cherkasin, E. Paolini, Y) solved  Steiner problem for some fractal set of points on the sides of an angle.

Some other works:

• •  Here we (C. Labourie, Y.) researched quasiminimal sets of codimension one. Particularly, we proved local finiteness in Euclidean spaces of dimensions 2 and 3.

  • Here we (D. Cherkashin, Y.) investigated the relationship between the uniqueness of a Steiner tree and the existence of a set for which it is a maximal distance minimizer. In this work we also constructed an example of MDM with infinite number of the corner points.

  • Here we (E. Stepanov , Y.) proved in a finite-dimensional normed space a self-contracted curve contained in a compact has a finite length.

• Non-exhaustive list of repressed Russian matematicians and physicists

• Color pages  and color pages with prisons 

• Prison Observation: the report on the results of the public monitoring of appeals regarding instances of torture commited by officers of the FSB directorate fo St Petersburg and the report on the results of the public examination of the fact and circumstances of the tortures of Viktor Filinkov and Igor Shishkin