# Student Research Supervision

## PhD Students

- Inga V. Ptitsyna, Closed Minimal Networks on Closed Surfaces of Constant Gaussian Curvature (join supervision with Anatoly T. Fomenko and Alexander O. Ivanov)
- Grigory A. Karpunin, Morse Theory of Minimal Networks
- Denis P. Il'yutko, Geometry of Locally Minimal and Extremal Networks in Normed Spaces
- Nikita S. Gusev, Multi-dimensional Polyhedron-Traces and Geometrical Variational Problems (joint supervision with Alexander O. Ivanov)
- Nataliya P. Strelkova, Minimal Networks on Surfaces of Polyhedra

## Undergraduate Research Subjects

- Local Minimal Networks on Riemannian Manifolds
- Morse Theory of Planar Minimal Trees
- Geometry of Locally Minimal and Extremal Networks in Normed Spaces
- Steiner Problem with Partially Free boundary
- Affine Space Transformation and Scalar Curvature of Surfaces
- Steiner Problem on Hexagonal Plane
- Closed Locally Minimal Networks on Tetrahedra
- Local Structure of Lunes of Shortest Networks
- Bifurcations of Closed Minimal Networks on Planar Tori under Deformations of Their Metrics
- Triangular Tilings for Weighted Binary Trees
- Closed Minimal Networks on Surface of Cube
- Properties of One-Cell Closed Locally Minimal Networks on 2-Dimensional Surfaces of Constant Negative Curvature
- Torricelli Points on 3-Plane
- Melzak's Algorithm on 3-Plane
- Closed Locally Minimal Networks on Convex Polyhedra
- Steiner Subratio and Steiner-Gromov Ratio on Euclidean Plane
- Stabilization Along Regular Curve
- Stabilization of Locally Minimal Forest
- Topological Properties of 1-Dimensional Gromov Minimal Filling
- Steiner Problem in Hyperspace
- Steiner Problem for Regular Polygon on Hyperbolic Plane
- Steiner Problem for Regular Polygon on Hyperbolic Sphere
- Minimal Fillings for Regular Polygon on Euclidean Plane
- Locally Minimal Networks Construction by Means of Linkages
- Transformations of Metric Preserving Minimal Filling Types
- Uniqueness of Steiner Problem Solution for General Boundaries
- Steiner Problem in Gromov-Hausdorff Space: the Case of 3-Pointed Metric Spaces
- Optimal Position of Compacts W.R.T. Euclidean Gromov-Hausdorff Metric
- Linear Connectivity of Spheres in Gromov-Hausdorff Space
- Convexity of Balls in Gromov-Hausdorff Space
- Properties of Mapping Taking Each Compact Metric Space to its Hyperspace