Address

Università degli Studi di Genova, Dipartimento di Matematica, Machine learning Genoa center, Genova (Italy)

Email

wadim DOT gerner AT edu DOT unige DOT it

Web

unige.it

Research Area

Stellarator designs, plasma fusion, topological fluid dynamics, calculus of variations

Publications

• Existence and characterisation of magnetic energy minimisers on oriented, compact Riemannian 3-manifolds with boundary in arbitrary helicity classes
  W. Gerner
  Ann. Global Anal. Geom. 58 (2020), no. 3, 267–285
  doi: 10.1007/s10455-020-09727-4

• Typical field lines of Beltrami flows and boundary field line behaviour of Beltrami flows on simply connected, compact, smooth manifolds with boundary
  W. Gerner
  Ann. Global Anal. Geom. 60 (2021), pages 65–82
  doi: 10.1007/s10455-021-09768-3
  Preprint arXiv:2005.06590

• Zero set structure of real analytic Beltrami fields
  W. Gerner
  J. Geom. Anal. (2021)
  doi: 10.1007/s12220-021-00633-0
  Preprint arXiv:2005.07620

• Isoperimetric problem for the first curl eigenvalue
  W. Gerner
  J. Math. Anal. Appl. 519 (2023), no. 2, Paper No. 126808
  doi: 10.1016/j.jmaa.2022.126808
  Preprint arXiv:2203.00718

• Existence and structure of symmetric Beltrami flows on compact 3-manifolds
  W. Gerner
  Differential Geometry and its Applications, Volume 78, October 2021, 101801
  doi: 10.1016/j.difgeo.2021.101801
  Preprint arXiv:2006.14507

• A unique continuation theorem for exterior differential forms on Riemannian manifolds with boundary
  W. Gerner
  Preprint arXiv:2207.02029

• Optimal metrics for the first curl eigenvalue on 3-manifolds
  A. Enciso, W. Gerner, and D. Peralta-Salas
  Calc. Var. Partial Differential Equations 64 (2025), no. 5, Paper No. 146, 58 pp.
  doi: 10.1007/s00526-025-02995-7
  Preprint arXiv:2305.06681

• Existence of optimal domains for the helicity maximisation problem among domains satisfying a uniform ball condition
  W. Gerner
  J. Math. Phys. 65 (2024), no. 8, Paper No. 083506, 12 pp.
  doi: 10.1063/5.0163183
  Preprint arXiv:2305.13642

• Properties of the Biot-Savart operator acting on surface currents
  W. Gerner
  SIAM J. Math. Anal. 56 (2024), no. 5, 6446–6482
  doi: 10.1137/23M1615693
  Preprint arXiv:2311.03108

• Optimal convex domains for the first curl eigenvalue in dimension three
  A. Enciso, W. Gerner, and D. Peralta-Salas
  Trans. Amer. Math. Soc. 377 (2024), no. 7, 4519–4540
  doi: 10.1090/tran/8914
  Preprint arXiv:2202.09204

• Properties of surface helicity and its optimisation
  W. Gerner
  Discrete Contin. Dyn. Syst. 49 (2026), 106–138
  doi: 10.3934/dcds.2025158
  Preprint arXiv:2408.00492

• Charged particle motion in a strong magnetic field: Applications to plasma confinement
  U. Boscain and W. Gerner
  Nonlinearity 38 (2025), no. 10, Paper No. 105017, 30 pp.
  doi: 10.1088/1361-6544/ae117a
  Preprint arXiv:2504.04165

• Kernel and image of the Biot-Savart operator and their applications in stellarator designs
  W. Gerner
  Preprint arXiv 2504.04176

• Quantitative Gaffney and Korn inequalities
  W. Gerner
  Preprint arXiv:2510.05870

• Influence of coil geometry and coil-plasma distance on the magnetic field approximation error
  W. Gerner
  Preprint arXiv:2510.06773

• Non-optimal domains for the helicity maximisation problem
  W. Gerner
  Preprint arXiv 2510.20533