Publications

Preprints.

1. M. Karpukhin, R. Kusner, P. McGrath, D. Stern, Embedded minimal surfaces in S^3 and B^3 via equivariant eigenvalue optimization. arXiv:2402.13121 

2. M. Karpukhin, A. Métras, I. Polterovich, Dirac Eigenvalue Optimisation and Harmonic Maps to Complex Projective Spaces. arXiv:2308.07875

Published and accepted articles.

1. M. Karpukhin, D. Stern, Existence of harmonic maps and eigenvalue optimization in higher dimensions. To appear in Inventiones Mathematicae. arXiv:2207.13635. DOI 10.1007/s00222-024-01247-3.

2. M. Karpukhin, M. Nahon, I. Polterovich, D. L. Stern, Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces. To appear in Journal of Diff. Geom. arXiv:2106.15043. 

3. M. Karpukhin, D. L. Stern, Min-max harmonic maps and a new characterization of conformal eigenvalues. To appear in J. Of EMS. arXiv:2004.04086. DOI 10.4171/JEMS/1401.

4. M. Karpukhin, D. L. Stern, From Steklov to Laplace: free boundary minimal surfaces with many boundary components. To appear in Duke Math. J. arXiv:2109.11029. 

5. M. Karpukhin, J. Lagacé, I. Polterovich, Weyl's law for the Steklov problem on surfaces with rough boundary. ARMA 247:5 (2023), 1 -  20. arXiv:2204.05294. DOI 10.1007/s00205-023-01912-6. 

6. M. Karpukhin, J. Lagacé, Flexibility of Steklov eigenvalues via boundary homogenisation. Annales mathématiques du Québec. arxiv:2207.02816. DOI 10.1007/s40316-022-00207-8. 

7. M. Karpukhin, A. Métras, Laplace and Steklov extremal metrics via n-harmonic maps.  J. of Geom. Analysis 32 (2022), article 154. arXiv:2103.15204. DOI 10.1007/s12220-022-00891-6 

8. M. Karpukhin, D. Vinokurov, The first eigenvalue of the Laplacian on orientable surfaces. Math. Zeitschrift 301  (2022), 2733 - 2746. arXiv:2106.00627. DOI 10.1007/s00209-022-03009-4  

9. M. Karpukhin, X. Zhu, Spherical conical metrics and harmonic maps to spheres. Transactions of AMS 375:5 (2022), 3325 - 3350. arXiv:2104.10304. DOI10.1090/tran/8578  

10. A. Girouard, M. Karpukhin, M. Levitin, I. Polterovich, The Dirichlet-to-Neumann map, the boundary Laplacian, and Hörmander's rediscovered manuscript.  J. of Spectral Theory 12:1 (2022), 195 - 225. arXiv:2102.06594. DOI 10.4171/JST/399  

11. M. Karpukhin, N. Nadirashvili, A. V. Penskoi, I. Polterovich, Conformally maximal metrics for Laplace eigenvalues on surfaces. Surveys in Differential Geometry 24:1 (2019), 205 - 256. arXiv:2003.02871. DOI 10.4310/SDG.2019.v24.n1.a6  

12. A. Girouard, M. Karpukhin, J. Lagacé, Continuity of eigenvalues and shape optimization for Laplace and Steklov problems. Geometric and Functional Analysis 31 (2021), 513 - 561. arXiv:2004.10784. DOI 10.1007/s00039-021-00573-5 

13. M. Karpukhin, V. Medvedev, On the Friedlander-Nadirashvili invariants of surfaces. Mathematische Annalen 379 (2021), 1767 - 1805. arXiv:1901.09443. DOI 10.1007/s00208-020-02094-2 

14. G. Cox, D. Jakobson, M. Karpukhin, Y. Sire, Conformal invariants from nodal sets II. Manifolds with boundary. J. of Spectral Theory 11 (2021), 387 - 409. arXiv:1905.06136. DOI 10.4171/JST/345 

15. M. Karpukhin, Index of minimal  surfaces and isoperimetric eigenvalue inequalities. Inventiones Mathematicae 223 (2021), 335 - 377. arXiv:1905.03174. DOI 10.1007/s00222-020-00992-5 

16. M. Karpukhin, On the Yang-Yau inequality for the first Laplace eigenvalue. Geometric and Functional Analysis 29:6 (2019), 1864 - 1885 arXiv:1902.03473. DOI 10.1007/s00039-019-00518-z 

17. M. Karpukhin, N. Nadirashvili, A. Penskoi and I. Polterovich, An isoperimetric inequality for Laplace eigenvalues on the sphere. Journal of Diff. Geom. 118:2 (2021), 313 - 333 arXiv:1706.05713. DOI 10.4310/jdg/1622743142  

18. D. Cianci, M. Karpukhin, V. Medvedev, On branched minimal immersions of surfaces by first eigenfunctions.  Annals of Global Analysis and Geometry 56:4 (2019), 667 - 690. arXiv:1711.05916. DOI 10.1007/s10455-019-09683-8 

19. M. Karpukhin, Steklov problem on differential forms. Canadian J. Math. 71:2 (2019), 417 - 435. arXiv:1705.08951. DOI 10.4153/CJM-2018-028-6 

20. M. Karpukhin, Bounds between Laplace and Steklov eigenvalues on nonnegatively curved manifolds. Electron. Res. Announc. Math. Sci. 24 (2017), 100 - 109. arXiv:1512.09038. DOI 10.3934/era.2017.24.011 

21. M. Karpukhin, Upper bounds for the first eigenvalue of the Laplacian on non-orientable surfaces. Int. Math. Res. Notes 20 (2016), 6200 - 6209. arXiv:1503.08493. DOI 10.1093/imrn/rnv345 

22. M. Karpukhin, Spectral properties of a family of minimal tori of revolution in five-dimensional sphere. Canadian Mathematical Bulletin, 58:2 (2015), 285 - 296. arXiv:1301.2483. DOI 10.4153/CMB-2015-006-0 

23. M. Karpukhin, Nonmaximality of extremal metrics on torus and Klein bottle. Sbornik: Mathematics, 204:12 (2013), 1728 - 1744. arXiv:1210.8122. DOI 10.1070/SM2013v204n12ABEH004358. 

24. M. Karpukhin, G. Kokarev, I. Polterovich, Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces. Annales de l'Institute Fourier, 64:6 (2014), 2481 - 2502. arXiv:1209.4869. DOI 10.5802/aif.2918. 

25. M. Karpukhin, Spectral properties of bipolar surfaces to Otsuki tori.  J. of Spectral Theory, 4:1 (2014), 87 - 111. arXiv:1205.6316. DOI 10.4171/JST/63.