Líneas de investigación / Research topics
- Problemas isoperimétricos y superficies que minimizan el área / Isoperimetric problems and area-minimizing surfaces
- Superficies de curvatura media constante / Constant mean curvature surfaces
- Problemas variacionales en espacios de medida métricos / Variational problems in metric-measure spaces
Equipos de investigación / Research grants
Libro / Book
Artículos / Papers
![[Mathscinet]](http://wpd.ugr.es/~geometry/seminar/img/icon/mathscinet.png "Mathscinet Profile")
![[zentralblatt]](http://wpd.ugr.es/~geometry/seminar/img/icon/zentralblatt.png "Zentralblatt profile")
- A note on the anisotropic Bernstein problem in $\mathbb{R}^3$
Proc. Amer. Math. Soc. Ser. B 11 (2024), 105-114.
- Compact anisotropic stable hypersurfaces with free boundary in convex solid cones
Calc. Var. Partial Differential Equations 62,
no. 6 (2023), 185.
- Area-minimizing properties of Pansu spheres in the sub-Riemannian 3-sphere
Joint with A. Hurtado
Adv. Calc. Var. 16,
no. 3 (2023), 689-704. [PDF]
- Stable capillary hypersurfaces and the partitioning problem in balls with radial weights
Nonlinear Anal. 233
(2023), 113291.
- Uniqueness results and enclosure properties for hypersurfaces with boundary in weighted cylinders
Joint with K. Castro
J. Math. Anal. Appl. 512, no. 1 (2022), 126143.
- Stable and isoperimetric regions in some weighted manifolds with boundary
Nonlinear Anal. 205
(2021), 112217.
- An instability criterion for volume-preserving area-stationary surfaces with singular curves in sub-Riemannian 3-space forms
Joint with A. Hurtado
Calc. Var. Partial Differential Equations 59 (2020), 165. [PDF]
- Intrinsic and extrinsic comparison results for isoperimetric quotients and capacities in weighted manifolds
Joint with A. Hurtado and V. Palmer
J. Math. Anal. Appl. 492, no. 2
(2020), 124488. [PDF]
- Parabolicity criteria and characterization results for submanifolds of bounded mean curvature in model manifolds with weights
Joint with A. Hurtado and V. Palmer
Nonlinear Anal. 192
(2020), 111681. [PDF]
- Strongly
stable surfaces in sub-Riemannian 3-space forms
Joint with A. Hurtado
Nonlinear Anal. 155
(2017), 115-139. [PDF]
- Existence, characterization and stability of Pansu spheres in sub-Riemannian 3-space forms
Joint with A. Hurtado
Calc. Var. Partial Differential
Equations 54,
no. 3 (2015), 3183-3227.
[PDF]
- Isoperimetric
and stable sets for log-concave perturbations of Gaussian
measures
Anal. Geom. Metr. Spaces 2,
no. 1 (2014), 328-358.
[PDF]
- Compact
stable hypersurfaces with free boundary in convex solid cones
with homogeneous densities
Joint with A. Cañete
Calc. Var. Partial Differential
Equations 51,
no. 3-4 (2014), 887-913. [PDF]
- Free
boundary stable hypersurfaces in manifolds with density and
rigidity results
Joint with K. Castro
J. Geom. Phys. 79
(2014), 14-28. [PDF]
- Complete
stable CMC surfaces with empty singular set in Sasakian
sub-Riemannian 3-manifolds
Calc. Var. Partial Differential
Equations 43,
no. 3-4 (2012), 311-345. [PDF]
- The
classification of complete stable area-stationary surfaces in
the Heisenberg group $\mathbb{H}^1$
Joint with A. Hurtado and M. Ritoré
Adv. Math. 224,
no. 2 (2010), 561-600. [PDF]
- Area-stationary
and stable surfaces in the sub-Riemannian Heisenberg group
$\mathbb{H}^1$
Joint with M. Ritoré
Mat. Contemp. 35
(2008), 185-203. [PDF]
- On
the isoperimetric problem in Euclidean space with density
Joint with V. Bayle, A. Cañete and F. Morgan
Calc. Var. Partial Differential
Equations 31,
no. 1 (2008), 27-46. [PDF]
- Area-stationary
surfaces inside the sub-Riemannian three-sphere
Joint with A. Hurtado
Math. Ann. 340,
no. 3 (2008), 675-708. [PDF]
- Area-stationary
surfaces in the Heisenberg group $\mathbb{H}^1$
Joint with M. Ritoré
Adv. Math. 219,
no. 2 (2008), 633-671. [PDF]
- Rotationally
invariant hypersurfaces with constant mean curvature in the
Heisenberg group $\mathbb{H}^n$
Joint with M. Ritoré
J. Geom. Anal. 16,
no. 4 (2006), 703-720. [PDF]
- Some
isoperimetric comparison theorems for convex bodies in
Riemannian manifolds
Joint with V. Bayle
Indiana Univ. Math. J. 54,
no. 5 (2005), 1371-1394. [PDF]
- Existence
and characterization of regions minimizing perimeter under a
volume constraint inside Euclidean cones
Joint with M. Ritoré
Trans. Amer. Math. Soc. 356,
no. 11 (2004), 4601-4622. [PDF]
- Isoperimetric
regions in rotationally symmetric convex bodies
Indiana Univ. Math. J. 52,
no. 5 (2003), 1201-1214. [PDF]
Otras publicaciones / Other papers
- A. Hurtado y C. Rosales, Estabilidad de superficies en la 3-esfera sub-riemanniana, Florentino García Santos: in memoriam, Editorial Universidad de Granada, volumen 224 (2011), 87-94.
- C. Rosales, The isoperimetric problem in the Heisenberg group $\mathbb{H}^1$, XV International Workshop on Geometry and Physics, Publicaciones de la RSME, volumen 11 (2007), 341-346.
- C. Rosales, Constant mean curvature surfaces in the Heisenberg group $\mathbb{H}^1$, XIV Fall Workshop on Geometry and Physics, Publicaciones de la RSME, volumen 10 (2006), 231-237.
- C. Rosales, Isoperimetric problems inside Euclidean convex domains, XIII Fall Workshop on Geometry
and Physics, Publicaciones de la RSME, volumen 9
(2005), 247-253.
- C. Rosales, Stable constant mean curvature hypersurfaces inside convex domains, Differential Geometry and its Applications, Proceedings 9th International Conference on Differential Geometry and its Applications, Matfyzpress, Charles University, Prague, Czech Republic, 2005, 161-173.
Tesis y tesina / Ph.D. thesis and minor thesis
Colaboradores / Collaborators
Estudiantes / Research training
