Research work – Manuel Ritoré

M. Ritoré, Isoperimetric inequalities in Riemannian manifolds, Progress in Mathematics 348, Birkhauser Verlag, 2023.
G. Giovannardi, M. Ritoré, The Bernstein problem for $(X,Y)$-Lipschitz surfaces in three-dimensional sub-Finsler Heisenberg groups, Commun. Contemp. Math. (to appear). arXiv:2105.02179.
M. Ritoré, On the geometry of metric spaces, Notices AMS 70, no. 9 (2023) 1417–1425 .
G. Gioannardi, J. Pozuelo, M. Ritoré, Area-minimizing horizontal graphs with low-regularity in the sub-Finsler Heisenberg group $\mathbb{H}^1$, New Trends in Geometric Analysis, RSME Springer Series 10, 2023, pp. 209–226.
S. Barbero, M. Ritoré, Extended-depth-of-focus wavefront design from pseudo-umbilical space curves, Journal of the Optical Society of America A 40, no. 10 (2023).
J. Pozuelo, M. Ritoré, Pansu-Wulff shapes in $\mathbb{H}^1$. Adv. Calc. Var. 16 , no. 1 (2023) 69–98. arXiv:2007.04683.
G. P. Leonardi, M. Ritoré, E. Vernadakis, Isoperimetric inequalities in unbounded convex bodies, Mem. Amer. Math. Soc. 276, no. 1354 (2022). arXiv:1606.03906.
G. Citti, G. Giovannardi, M. Ritoré, Variational formulas for curves of fixed degree. Adv. Differential Equations 27, no. 5-6 (2022) 333–384. arXiv:1902.04015.
G. Giovannardi, M. Ritoré, Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group $\mathbb{H}^1$. J. Differential Equations 302 (2021) 474–495. arXiv:2010.14882.
G. Citti, G. Giovannardi, M. Ritoré, Variational formulas for submanifolds of fixed degree. Calc. Var. PDE 60, no. 6 (2021) Paper No. 233, 44 pp. arXiv:1905.05131.
S. Nicolussi Golo, M. Ritoré, Area-minimizing cones in the Heisenberg group $\mathbb{H}^1$, Annales Fennici Mathematica 46, no. 2 (2021) 945–956. arXiv:2008.0427.
M. Ritoré, Tubular neighborhoods in the sub-Riemannian Heisenberg groups, Adv. Calc. Var. 14, no. 1 (2021) 1-36. arXiv:1703.01592.
S. Barbero, M. Ritoré, Circle involute as an optimal scan path, minimizing acquisition time, in surface topography, Surface Topography: Metrology and Properties, 7 no. 3 (2019).
M. Ritoré, J. Yepes Nicolás, Brunn-Minkowski inequalities in product metric measure spaces, Adv. Math. 325 (2018) 824–863. arXiv:1704.07717.
M. Ritoré, E. Vernadakis, Large isoperimetric regions in the product of a compact manifold with Euclidean space. Adv. Math. 306 (2017) 958-972. arXiv:1312.1581.
M. Ritoré, Continuity of the isoperimetric profile of a complete Riemannian manifold under sectional curvature conditions. Rev. Mat. Iberoam. 33, no. 1 (2017) 239-250. arXiv:1503.07014.
M. Ritoré, E. Vernadakis, Isoperimetric inequalities in conically bounded convex bodies, J. Geom. Anal. 26, no. 1 (2016) 474-498. arXiv:1404.0370.
M. Galli, M. Ritoré, Regularity of $C^1$ surfaces with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds, Calc. Var. PDE 54, no. 3 (2015) 2503-2516. arXiv:1501.07246.
M. Galli, M. Ritoré, Area-stationary and stable surfaces of class $C^1$ in the sub-Riemannian Heisenberg group $\mathbb{H}^1$, Adv. Math. 285 (2015) 737–765. arXiv:1410.3619.
M. Ritoré, E. Vernadakis, Isoperimetric inequalities in convex cylinders and cylindrically bounded convex bodies, Calc. Var. PDE 54, no. 1 (2015) 643-663. arXiv:1401.3542.
M. Ritoré, E. Vernadakis, Isoperimetric inequalities in Euclidean convex bodies, Transactions Amer. Math. Soc. 367 (2015) 4983-5014. arXiv:1302.4588.
M. Galli, M. Ritoré, Existence of isoperimetric regions in contact sub-Riemannian manifolds, Journal of Mathematical Analysis and Applications 397 (2013) 697-714. Accepted Author Manuscript.
A. Hurtado, M. Ritoré, V. Palmer, Comparison results for capacity, Indiana Univ. Math. J. 61 (2012), 539-555. arXiv:1012:0487
M. Ritoré, A proof by calibration of an isoperimetric inequality in the Heisenberg group $\mathbb{H}^n$, Calc. Var. PDE 44 no. 1-2 (2012), 47-60. (preprint)
A. Hurtado, M. Ritoré, C. Rosales, The classification of complete stable area-stationary surfaces in the Heisenberg group $\mathbb{H}^1$, Adv. Math. 224 no. 2 (2010) 561-600. (preprint)
M. Ritoré, C. Sinestrari, Mean curvature flow and isoperimetric inequalities, Advanced Courses in Mathematics – CRM Barcelona, Birkhaüser, 2010. ISBN: 978-3-0346-0212-9.
M. Ritoré, Examples of area-minimizing surfaces in the sub-Riemannian Heisenberg group $\mathbb{H}^1$ with low regularity, Calc. Var. PDE 34 no. 2 (2009) 179-192. (preprint)
M. Ritoré, C. Rosales, Area-stationary surfaces in the Heisenberg group $\mathbb{H}^1$, Adv. Math. 219 no. 2 (2008) 633-671. (preprint)
A. Cañete, M. Ritoré, The isoperimetric problem in complete annuli of revolution with increasing Gauss curvature, Proc. Royal Society Edinburgh 138 no. 5 (2008) 989-1003. (preprint)
J. Choe, M. Ritoré, The relative isoperimetric inequality in Cartan-Hadamard 3-manifolds, J. Reine Angew. Math. 605 (2007) 179-191.
J. Choe, M. Ghomi, M. Ritoré, The relative isoperimetric inequality outside a convex domain in $\mathbb{R}^n$, Calc. Var. PDE 29 no. 4 (2007) 421-429.
M. Ritoré, C. Rosales, Rotationally invariant hypersurfaces with constant mean curvature in the Heisenberg group $\mathbb{H}^n$, J. Geom. Anal. 16, no. 4 (2006) 703-720.
J. Choe, M. Ghomi, M. Ritoré, Total positive curvature of hypersurfaces with convex boundary, J. Differential Geom. 72, no. 1 (2006) 129-147.
M. Ritoré, Optimal isoperimetric inequalities for three-dimensional Cartan-Hadamard manifolds, Global theory of minimal surfaces, 395-404, Clay Math. Proc., 2, Amer. Math. Soc., Providence, RI, 2005.
F. Morgan, M. Ritoré, Geometric measure theory and the proof of the double bubble conjecture, Global theory of minimal surfaces, 1-18, Clay Math. Proc., 2, Amer. Math. Soc., Providence, RI, 2005.
A. Cañete, M. Ritoré, Least-perimeter partitions of the disk into three regions of given areas, Indiana Univ. Math. J. 53, no. 3 (2004) 883-904.
M. Ritoré, C. Rosales, Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones, Trans. Amer. Math. Soc. 356, no. 11 (2004) 4601-4622.
F. Pacard, M. Ritoré, From constant mean curvature hypersurfaces to the gradient theory of phase transitions, J. Differential Geom. 64, no. 3 (2003) 359-423.
M. Ritoré, A. Ros, Some updates on isoperimetric problems, Math. Intelligencer 24, no. 3 (2002) 9-14.
F. Morgan, M. Ritoré, Isoperimetric regions in cones, Trans. Amer. Math. Soc. 354 (2002), no. 6, 2327-2339.
M. Hutchings, F. Morgan, M. Ritoré, A. Ros, Proof of the double bubble conjecture, Ann. Math. (2) 155 (2002), no. 2, 459-489.
M. Ritoré, The isoperimetric problem in complete surfaces with nonnegative curvature, J. Geom. Anal. 11 (2001), no. 3, 509-517.
M. Ritoré, Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces, Comm. Anal. Geom. 9 (2001), no. 5, 1093-1138.
M. Hutchings, F. Morgan, M. Ritoré, A. Ros, Proof of the double bubble conjecture, Electron. Res. Announc. Amer. Math. Soc. 6 (2000) 45-49.
M. do Carmo, M. Ritoré, A. Ros, Index one minimal surfaces in Real Projective Spaces, Comment. Math. Helvetici 75 (2000), no. 2, 247-254.
R. Pedrosa, M. Ritoré, Isoperimetric domains in the Riemannian product of a circle with a simply connected space form and applications to free boundary problems, Indiana Univ. Math. J. 48 (1999) 1357-1394.
M. Ritoré, Index one minimal surfaces in flat three-space forms, Indiana Univ. Math. J. 46, no. 4 (1997) 1137-1153.
F. J. López, M. Ritoré, F. Wei, A characterization of Riemann’s minimal surfaces, J. Differential Geom. 47(1997) 376-397.
M. Ritoré, Stable periodic projective planes, Proc. Amer. Math. Soc. 124 (1996) 3851-3856.
M. Ritoré, Applications of compactness results for harmonic maps to stable constant mean curvature surfaces, Math. Z. 226 (1997) 465-481.
M. Ritoré, Examples of constant mean curvature surfaces obtained from harmonic maps to the two sphere, Math. Z. 226 (1997) 127-146.
M. Ritoré, A. Ros, The spaces of index one minimal surfaces and constant mean curvature surfaces embedded in flat three manifolds, Transactions Amer. Math. Soc. 348 (1996) 391-410.
M. Ritoré, A. Ros, Stable constant mean curvature tori and the isoperimetric problem in three-space forms, Comment. Math. Helvetici 67 (1992) 293-305.
M. Ritoré, Superficies con curvatura media constante, Tesis doctoral, Universidad de Granada, 1994.