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