Papers

Complete CMC-1 surfaces in hyperbolic space with arbitrary complex structure.

Alarcon, Antonio & Castro-Infantes, Ildefonso & Hidalgo, Jorge.
Commun. Contemp. Math., in press. arXiv:2306.14482.

Helicoidal minimal surfaces in the 3-sphere: An approach via spherical curves.

Castro, Ildefonso & Castro-Infantes, Ildefonso & Castro-Infantes, Jesús.
Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 77 (2024). https://doi.org/10.1007/s13398-024-01574-3 arXiv:2303.08043.

Spherical curves whose curvature depends on distance to a great circle.

Castro, Ildefonso & Castro-Infantes, Ildefonso & Castro-Infantes, Jesús.
New Trends in Geometric Analysis. RSME Springer Series, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-031-39916-9_2 arXiv:2111.00458.

Interpolation by complete minimal surfaces whose Gauss map misses two points.

Castro-Infantes, Ildefonso
J Geom Anal 31, 5395–5417 (2021). https://doi.org/10.1007/s12220-020-00484-1 arXiv:1912.12429.

Carleman approximation by conformal minimal immersions and directed holomorphic curves.

Castro-Infantes, Ildefonso & Chenoweth, Brett.
J. Math. Anal. Appl. 484 (2020), no. 2, 123756. arXiv:1906.03215.

Curves in Lorentz-Minkowski plane with curvature depending on their position.

Castro, Ildefonso & Castro-Infantes, Ildefonso & Castro-Infantes, Jesús.
Open Math. 2020; 18 (1): 749–770. arXiv:1806.09187.

Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers.

Castro, Ildefonso & Castro-Infantes, Ildefonso & Castro-Infantes, Jesús.
Open Math. 2018; 16 (1): 747–766.

Interpolation and optimal hitting for complete minimal surfaces with finite total curvature.

Alarcón, Antonio & Castro-Infantes, Ildefonso & López, Francisco J.
Calc. Var. (2019) 58: 21. https://doi.org/10.1007/s00526-018-1465-0 arXiv1712.04727.
Correction: Calc. Var. 59, 178 (2020). arxiv2004.01617

Interpolation by conformal minimal surfaces and directed holomorphic curves.

Alarcón, Antonio & Castro-Infantes, Ildefonso.
Analysis & PDE 12-2 (2019), 561–604. DOI 10.2140/apde.2019.12.561 arXiv1701.04379.

Complete minimal surfaces densely lying in arbitrary domains of ℝⁿ.

Alarcón, Antonio & Castro-Infantes, Ildefonso.
Geom. Topol. 22 (2018), no. 1, 571–590. arXiv1611.05029.

New plane curves with curvature depending on distance from the origin.

Castro, Ildefonso & Castro-Infantes, Ildefonso & Castro-Infantes, Jesús.
Mediterr. J. Math. (2017) 14: 108 DOI: 10.1007/s00009-017-0912-z.

Plane curves with curvature depending on distance to a line.

Castro, Ildefonso & Castro-Infantes, Ildefonso.
Diff. Geom. Appl. 44 (2016), 77–97.

A geometric application of Runge's theorem

Castro-Infantes, Ildefonso.
Reports@SCM, Vol 2, No 1 (2016), 21–32.