RESEARCH

RESEARCH INTEREST

Differential Geometry
Metric Foliations
Geometric Analysis

Geometric and Differential Topology
Group Actions
Geometric Group Theory

Here you find a list of open problems in the study of the geometry and topology of RCD-spaces.

PUBLICATIONS

A-Foliations of codimension two on compact simply-connected manifolds
arXiv:1903.07191 [math.DG], in Math. Z. 304, Article No. 63, 1--32, 2023.
Yamabe problem in the presence of singular Riemannian Foliations (with Juan Carlos Fernández and Raquel Perales)
arXiv:2202.13109 [math.AP], in Calc. Var. Partial Differential Equations, vol. 62, Article Number: 26, 2023.
Core reduction for singular Riemannian foliations and applications to positive curvature (with Adam Moreno) arXiv:2011.05303 [math.DG], in Ann. Global Anal. Geom., vol. 62, pp. 617–634, 2022.
Torus actions on Alexandrov 4-spaces (with Jesús Núñez-Zimbrón, and Masoumeh Zarei) arXiv:1902.09402 [math.DG], in J. Geom. Anal. 32, Article Number: 214, 2022.
Short survey on the existence of slices for the space of Riemannian metrics (with Jan-Bernhard Kordaß) arXiv:1904.07031 [math.DG], in Contemporary Mathematics, vol. 75, "Mexican Mathematicians in the World: Trends and Recent Contributions", pp. 65-84, 2021.
Bundles with even-dimensional spherical space form as fibers and fiberwise quarter pinched Riemannian metrics (with Martin Günther, Karla Garcia, and Jan-Bernhard Kordaß), arXiv:2004.02518 [math.GT] Proc. A. M. S., vol. 149 (12), pp. 5407-5416, 2021.
Integral foliated simplicial volume and circle foliations (with Caterina Campagnolo) arXiv:1910.03071 [math.GT], in J. Topol. Anal., 2021.
Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions (with Fernando Galaz-Garcia), arXiv:1609.06125 [math.DG] in Proc. A. M. S., vol. 148, (7), pp. 3087–3097, 2020.

PREPRINTS

Myers-Steenrod theorems for metric and singular Riemannian foliations (with with Fernando Galaz-García)
arXiv:2407.03534 [math.DG].
Cohomogeneity one RCD-spaces (with Jesús Núñez-Zimbrón, and Jaime Santos-Rodríguez)
arXiv:2405.09448 [math.MG].
Collapsing regular Riemannian foliations with flat leaves
arXiv:2403.11602 [math.DG]
Singular Riemannian Foliations, variational problems and Principles of Symmetric Criticalities (with Marcos M. Alexandrino, Leonardo F. Cavenaghi, and Marcelo K. Inagaki)
arXiv:2311.07058 [math.DG].

IN PREPARATION

Smooth 2-torus actions on the 5-sphere, andnonnegative curvature (with Fernando Galaz-García and Martin Kerin).
Myres-Steenrod theorem for metric submetries and applications to singular Riemannian foliations (with Fernando Galaz-Garcia).

STUDENTS

Juan Flores Torres (Master Degree, UNAM )
"Moduli space of bi-invariant metrics" arXiv:2305.14475 [math.DG], en Bol. Soc. Mat. Mex., vol. 30, 30, (2), Paper No. 49, 2024.