Publications

Publication list

1. Rigidity of bounded type Siegel polynomials, (with J. Yang), 34 pp, 2025 [pdf]
   
   

2. Density of stable interval translations maps, (with L. Staresinic and S. van Strien), 87 pp, 2024 (submitted) [pdf]

3. Stability of reverse isoperimetric inequalities in the plane: area, Cheeger, and inradius, (with K. Tatarko), 17 pp, 2024 (submitted) [pdf]
   
   

4. The Blaschke rolling theorem in Riemannian manifolds of bounded curvature, 20 pp, 2024 (submitted) [pdf]
   
   

5. Reverse isoperimetric problems under curvature constraints, (with K. Tatarko), 37 pp, 2023 (submitted) [pdf]
   
   

6. Rigidity of Newton dynamics, (with D. Schleicher),
   Advances in Mathematics, 408, 2022.  [open access link]

7. The Dynamics  of Complex Box Mappings, (with T. Clark, O. Kozlovski, and S. van Strien),
   Arnold  Mathematical Journal,  8:319-410,  2022.  [open access link]  

8. Puzzles and the Fatou-Shishikura injection for rational Newton maps, (with R. Lodge, D. Schleicher, and M. Sowinski),
   Transactions of the American Mathematical Society, 374:2753-2784, 2021. [link]

9. A hyperbolic view of the Seven Circles Theorem,  (with R. Schwartz),
   The Mathematical Intelligencer, 42:61-65, 2020.

** Watch a beautiful explanation of our proof on YouTube! ** [YouTube Link] 

10. A sausage body is a unique solution for a reverse isoperimetric problem, (with R. Chernov and K. Tatarko),
    Advances in Mathematics, 353:431-445, 2019. [pdf]

11. A combinatorial classification of postcritically fixed Newton maps, (with Ya. Mikulich, J. Rueckert, and D. Schleicher),
    Ergodic Theory and Dynamical Systems, 39(11):2983-3014, 2019.

12. Archimedean toroidal maps and their minimal almost regular covers, (with Y. Haidamaka, M. Mixer, and M. Skoryk),
    Ars Mathematica Contemporanea, 17(2):493-514, 2019.

13. Inradius estimates for convex domains in 2-dimensional Alexandrov spaces,
    Analysis and Geometry in Metric Spaces, 6:165-173, 2018.

14. On the solution of reverse Dido's problem for convex surfaces of revolution,
    Dopov. Nac. Akad. Nauk Ukr., (4):7-12, 2016. 

15. Extreme properties of curves with bounded curvature on a sphere, (with A. Borisenko),
    Journal of Dynamical and Control Systems, 21(3):311-327, 2015.

16. Comparison theorem for the support functions of hypersurfaces, (with A. Borisenko),
    Dopov. Nats. Akad. Nauk Ukr., (3):11-16, 2015. (arXiv:1402.2691 [math.DG])

17. Some sharp estimates for convex hypersurfaces of pinched normal curvature,
    Journal of Mathematical Physics, Analysis, Geometry, 11(2):111-122, 2015.

18. Minimal covers of equivelar toroidal maps, (with M. Mixer),
    Ars Mathematica Contemporanea, 9(2):77-91, 2015.

19. Isoperimetric inequality for curves with curvature bounded below, (with A. Borisenko),
    Mathematical Notes, 95(5):590-598, 2014.

20. About the isoperimetric property of $\lambda$-convex lunes on the Lobachevsky plane,
    Dopov. Nats. Akad. Nauk Ukr., (11):11-15, 2014. (arXiv:1402.2688 [math.DG])

21. Closeness to spheres of hypersurfaces with normal curvature bounded below, (with A. Borisenko),
    Sbornik: Mathematics, 204(11):1565-1583, 2013.

22. About an angle comparison theorem for closed curves, (with A. Borisenko),
    Dopov. Nats. Akad. Nauk Ukr., (6):7-11, 2011.

Patents [link]

1. S. Glushakov, K. Drach, V. Shevtsova, I. Kotenko, L. Polyakova, O. Leonov. Multiscale graph-based analysis and visualization of clinical data. US Patent Application US20250201368-A1,  2025. [pdf USPTO]
   
   

2. S. Glushakov, K. Drach, V. Shevtsova, I. Kotenko, L. Polyakova, O. Leonov. Automatic selection of optimal graphs with robust geometric properties in graph-based discovery of geometry of clinical data. US Patent US12278003B2,  2025.  [pdf USPTO]
   
   

3. S. Glushakov, K. Drach, V. Shevtsova, I. Kotenko, L. Polyakova. Graph-based discovery of geometry of clinical data to reveal communities of clinical trials subjects, US Patent US11789970B2, 2023. [pdf Google Patents]
   
   

4. S. Glushakov, V. Balon, I. Kotenko, A. Rekalo, K. Drach, B. Chornomaz, V. Shevtsova. Systems and methods for topology-based clinical data mining, US Patent US11069447B2, 2021.  [pdf Google Patents]

PhD Thesis

Extreme bounds for complete hypersurfaces in Riemannian spaces, B. Verkin Institute for Low Temperature Physics and Engineering of the NAS of Ukraine, Kharkiv, 2016. [pdf] 

Manuscripts

(with O. Shugailo and A. Yampolsky) The canonical theory of second order curves: a tutorial for 1st year bachelor students in mathematics and computer science, V. N. Karazin Kharkiv National University, Kharkiv, 2020. (link, in Ukrainian)

Conics associated with triangles, or how Poncelet meets Morley, arXiv:1410.4574 [math.MG]

(with Yu. Eremenko and A. Krymova) Uniquely constructed figures on the sphere, 2014 (link, in Ukrainian)