RESEARCH INTERESTS:
Differential Geometry. Geometric Analysis.
Lagrangian submanifolds.
Mean curvature flow.
Weingarten surfaces.
CMC surfaces.

PUBLICATIONS (papers, proceedings and preprints)

48| Carretero, Paula; Castro, Ildefonso
Rotational surfaces with prescribed curvatures.
arXiv:2312.14672 [math.DG]
47| Carretero, Paula; Castro, Ildefonso
A Geometric Characterization of The Quadric Surfaces of Revolution.
Romanian Journal of Mathematics and Computer Science, vol.13 2023, Issue 2 - Special Issue "Proceedings of the International Conference Riemannian Geometry and Applications - RIGA 2023", p. 76-82.
46| Castro, Ildefonso; Castro-Infantes, Ildefonso; Castro-Infantes, Jesús
Helicoidal minimal surfaces in the 3-sphere: An approach via spherical curves.
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 [math.DG]
45| Carretero, Paula; Castro, Ildefonso
A new approach to rotational Weingarten surfaces.
Mathematics 2022, 10, 578. https://doi.org/10.3390/math10040578
arXiv:2112.15395 [math.DG]
44| Castro, I., Castro-Infantes, I., Castro-Infantes, J. (2023).
Spherical Curves Whose Curvature Depends on Distance to a Great Circle.
In: Alarcón, A., Palmer, V., Rosales, C. (eds) 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 [math.DG]
43| Castro, Ildefonso; Castro-Infantes, Ildefonso; Castro-Infantes, Jesús
Prescribing Curvature to Spherical Helicoidal Surfaces.
Riemannian Geometry and Applications, Proceedings RIGA 2021.
Adela Mihai and Ion Mihai  Editors.  pp 5-16.
42| Castro, Ildefonso; Castro-Infantes, Ildefonso; Castro-Infantes, Jesús
On a Problem of David Singer about Prescribing Curvature for Curves.
Twenty First International Conference on Geometry, Integrability and Quantization
June 3-8, 2019, Varna, Bulgaria Ivaïlo M. Mladenov, Vladimir Pulov and Akira Yoshioka Editors.  Avangard Prima, Sofia 2020, pp 100-117. doi:10.7546/giq-21-2020-100-117.
41| Castro, Ildefonso; Castro-Infantes, Ildefonso; Castro-Infantes, Jesús
Curves in Lorentz-Minkowski plane with curvature depending on their position.
Open Math. 2020; 18: 749-770. arXiv:1806.09187 [math.DG].
40| Castro, Ildefonso; Castro-Infantes, Ildefonso; Castro-Infantes, Jesús
Curves in Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers.
Open Math. 2018; 16: 747-766.
39| Castro, Ildefonso; Lerma, Ana M.; Miquel,Vicente
Evolution by mean curvature flow of Lagrangian spherical surfaces in complex Euclidean plane. J. Math. Anal. Appl. 462 (2018), 637–647
https://doi.org/10.1016/j.jmaa.2018.02.033  arXiv:1603.03229 [math.DG]
38| Castro, Ildefonso; Lerma, Ana M.
Lagrangian translators under mean curvature flow
Proc. XI Encuentro Andaluz de Geometría (IMUS Sevilla, 15 de mayo de 2015), 59-65.
Alfonso Carriazo et al. (Ed.) 2017. ISBN 978-84-17293-09-3.
37| Castro, Ildefonso; Castro-Infantes, Ildefonso; Castro-Infantes, Jesús
New plane curves with curvature depending on distance from the origin.
Mediterr. J. Math. (2017) 14: 108  DOI: 10.1007/s00009-017-0912-z
36| Castro, Ildefonso; Lerma, Ana M.
Lagrangian homothetic solitons for the inverse mean curvature flow.
Results in Maths. 71 (2017), 1109-1125
DOI 10.1007/s00025-016-0574-3 arXiv:1511.03826 [math.DG]
35| Castro, Ildefonso; Castro-Infantes, Ildefonso
Plane curves with curvature depending on distance to a line.
Diff. Geom. Appl. 44 (2016), 77-97
34| Castro, Ildefonso; Lerma, Ana M.
The Clifford torus as a self-shrinker for the Lagrangian mean curvature flow
International Mathematics Research Notices 2014 (2014), 1515–1527
doi:1093/imrn/rns264 arXiv:1202.2555 [math.DG]
33| Castro, Ildefonso; Lerma, Ana M.
A new construction of Lagrangians in the complex Euclidean plane in terms of planar curves
 Journal of Geometry and Physics 75 (2014), 162-172 arXiv:1307.2152
32| Castro, Ildefonso; Lerma, Ana M.
Lagrangian mean curvature flow
Pure and Applied Differential Geometry - PADGE 2012, In Memory of Franki Dillen, 72-80.
Joeri Van der Veken, Ignace Van de Woestyne, Leopold Verstraelen, Luc Vranken (Eds.),  Shaker Verlag, Aachen, 2013. ISBN: 978-3-8440-2363-3.
31| Castro, Ildefonso; Lerma, Ana M.
Solitons for Lagrangian mean curvature flow
Proc. Int. Meeting on Differential Geometry (Córdoba, November 15-17, 2010), 49-70.
Ediciones Don Folio, Córdoba, 2012. ISBN 978-84-15105-91-6.
30| Castro, Ildefonso; Lerma, Ana M.
Translating solitons for Lagrangian mean curvature flow in complex Euclidean plane
Internat. J. Math.  23, No. 10 (2012), 1250101 (16 pages) arXiv:1007.1886 [math.DG]
29| Castro, Ildefonso; Torralbo, Francisco; Urbano, Francisco
On Hamiltonian stationary Lagrangian spheres in non-Einstein Kaehler surfaces
Math. Z. 271 (2012), 257-270  arXiv:0706.4390 [math.DG]
28| Anciaux, Henri; Castro, Ildefonso
Construction of Hamiltonian-minimal Lagrangian submanifolds in complex Euclidean space.
Results Math. 60 (2011), 325–349 [math.DG]
27| Castro, Ildefonso; Lerma, Ana M.
Hamiltonian stationary self-similar solutions for Lagrangian mean curvature flow in complex Euclidean plane
Proc. Amer. Math. Soc. 138 (2010), 1821-1832 arXiv:0906.3117 [math.DG]
26| Castro, Ildefonso
Hamiltonian minimal Lagrangian spheres in the product of spheres
Symposium on the differential geometry of Submanifolds, 43-50,
Luc Vrancken (Ed.), 2007. ISBN: 978-1-8479-9016-7
25| Castro, Ildefonso
Minimal surfaces in  S^2  x  S^2
Pure and Applied Differential Geometry - PADGE 2007, 39-47,
Franki Dillen, Ignace Van de Woestyne (Eds.),  Shaker Publishing , 2007.
ISBN: 978-3-8322-6759-9
24| Castro, Ildefonso; Urbano, Francisco
Minimal Lagrangian surfaces in  S^2 x S^2.
Communications in Analysis and Geometry 15 (2007), 217-248  math.DG/0601637
23| Castro, Ildefonso; Chen, Bang-Yen
Lagrangian surfaces in complex Euclidean plane via spherical and hyperbolic curves.
Tohoku Math. J. 58 (2006), 565-579 math.DG/0603368
22| Castro, Ildefonso; Li, Haizhong.; Urbano, Francisco
Hamiltonian minimal Lagrangian submanifolds in complex space forms.
Pacific Journal of Mathematics 227 (2006), 43-65. math.DG/0412046
21| Anciaux, Henri; Castro, Ildefonso; Romon, Pascal
Lagrangian submanifolds foliated by (n-1)-spheres in R^2n.
Acta Math. Sinica 22 (2006), 1197-1214. math.DG/0401372v1
20| Castro, Ildefonso; Montealegre, Cristina R.
A family of surfaces with constant curvature in Euclidean four space.
Soochow Journal of Mathematics 30 (2004),  293-301
(Special volume in honour of B.Y. Chen).
19| Castro, Ildefonso; Urbano, Francisco
A characterization of the Lagrangian pseudosphere.
Proc. Amer. Math. Soc. 132 (2004),  1797-1804. Abstract
18| Castro, Ildefonso; Urbano, Francisco  
On a new construction of special Lagrangian immersions in complex Euclidean space.
Quart. J. Math. 55 (2004),  253-265.  (Oxford University Press). math.DG/0403108
17| Castro, Ildefonso  
Lagrangian surfaces with circular ellipse of curvature in complex  space forms.
Math. Proc. Cambridge Philos. Soc. 136 (2004),  239-245.  math.DG/0210134
16| Castro, I.; Montealegre, Cristina R.; Urbano, Francisco
Minimal Lagrangian submanifolds in the complex hyperbolic space.
Illinois Journal of Mathematics, 46 (2002), 695-721
15| Castro, Ildefonso; Vrancken, Luc
Minimal Lagrangian submanifolds in CP³ and the sinh-Gordon equation.
Results Math. 40 (2001), no. 1-4, 130-143.
14| Castro, Ildefonso; Montealegre, Cristina R.  
Lagrangian submanifolds with zero scalar curvature in complex Euclidean space.
Geom. Dedicata 86 (2001), no. 1-3, 179-183.
13| Castro, I.; Montealegre, Cristina R.; Urbano, Francisco
Closed conformal vector fields and Lagrangian submanifolds in complex space forms.
Pacific J. Math.199 (2001), no. 2, 269-302.
12| Castro, Ildefonso; Urbano, Francisco
Willmore surfaces of R⁴ and the Whitney sphere.
Ann. Global Anal. Geom. 19 (2001), no. 2, 153-175.
11| Castro, Ildefonso
The Lagrangian version of a theorem of J. B. Meusnier.
Summer School on Differential Geometry (Coimbra, 1999), 83-89,
Univ. Coimbra, Coimbra,1999.
10| Castro, Ildefonso
On the Lagrangian catenoid.
Geometry and topology of submanifolds, IX (Valenciennes/Lyon/Leuven, 1997), 74-79,
World Sci. Publishing, River Edge, NJ, 1999.
09| Castro, Ildefonso; Urbano, Francisco
On a minimal Lagrangian submanifold of Cⁿ foliated by spheres.
Michigan Math. J. 46 (1999), no. 1, 71-82.
08| Castro, I.  
Minimal Lagrangian submanifolds in complex Euclidean space.
Proceedings of the 1st International Meeting on Geometry and Topology (Braga, 1997), 43-49 (electronic),
Cent. Mat. Univ. Minho, Braga, 1998.
07| Castro, Ildefonso
Lagrangian spheres in the complex Euclidean space satisfying a geometric equality.
Geom. Dedicata 70 (1998), no. 2, 197-208.
06| Castro, Ildefonso; Urbano, Francisco
Examples of unstable Hamiltonian-minimal Lagrangian tori in C².
Compositio Math. 111 (1998), no. 1, 1-14.
05| Castro, Ildefonso; Urbano, Francisco
On twistor harmonic surfaces in the complex projective plane.
Math. Proc. Cambridge Philos. Soc. 122 (1997), no. 1, 115-129.
04| Castro, Ildefonso
Lagrangian surfaces with conformal Maslov form. (In collaboration with Francisco Urbano).
Geometry and topology of submanifolds, VIII (Brussels, 1995/Nordfjordeid, 1995), 46-55, World Sci. Publishing, River Edge, NJ, 1996.
03| Castro, Ildefonso; Urbano, Francisco
Twistor holomorphic Lagrangian surfaces in the complex projective and hyperbolic planes.
Ann. Global Anal. Geom. 13 (1995), no. 1, 59-67.
02| Castro, Ildefonso; Urbano, Francisco
New examples of minimal Lagrangian tori in the complex projective plane.
Manuscripta Math. 85 (1994), no. 3-4, 265-281.
01| Castro, Ildefonso; Urbano, Francisco
Lagrangian surfaces in the complex Euclidean plane with conformal Maslov form.
Tohoku Math. J. (2) 45 (1993), no. 4, 565-582.