• 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.


  1. 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).

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. Integral foliated simplicial volume and circle foliations (with Caterina Campagnolo) arXiv:1910.03071 [math.GT], in J. Topol. Anal., 2021.

  7. 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.


  1. A-Foliations of codimension two on compact simply-connected manifolds
    arXiv:1903.07191 [math.DG].


  1. Smooth 2-torus actions on the 5-sphere, andnonnegative curvature (with Fernando Galaz-Garica and Martin Kerin).

  2. Myres-Steenrod theorem for metric submetries and applications to singular Riemannian foliations (with Fernando Galaz-Garcia).

  3. Foliated principle of symmetric criticality and an application to orbit-like singular riemannian foliations.