Metric Geometry of Spaces of Persistence Diagrams
(2024)
Journal Article
Che, M., Galaz Garcia, F., Guijarro, L., & Membrillo Solis, I. (online). Metric Geometry of Spaces of Persistence Diagrams. Journal of Applied and Computational Topology, https://doi.org/10.1007/s41468-024-00189-2
All Outputs (30)
Kurdyka–Łojasiewicz functions and mapping cylinder neighborhoods (2024)
Journal Article
Cibotaru, D., & Galaz-García, F. (online). Kurdyka–Łojasiewicz functions and mapping cylinder neighborhoods. Annales de l'Institut Fourier, https://doi.org/10.5802/aif.3656Kurdyka–Łojasiewicz (KŁ) functions are real-valued functions characterized by a differential inequality involving the norm of their gradient. This class of functions is quite rich, containing objects as diverse as subanalytic, transnormal or Morse fu... Read More about Kurdyka–Łojasiewicz functions and mapping cylinder neighborhoods.
Basic metric geometry of the bottleneck distance (2024)
Journal Article
Che, M., Galaz-García, F., Guijarro, L., Membrillo Solis, I., & Valiunas, M. (2024). Basic metric geometry of the bottleneck distance. Proceedings of the American Mathematical Society, 152(8), 3575-3591. https://doi.org/10.1090/proc/16776Given a metric pair (X, A), i.e. a metric space X and a distinguished closed set A ⊂ X, one may construct in a functorial way a pointed pseudometric space D∞(X, A) of persistence diagrams equipped with the bottleneck distance. We investigate the basi... Read More about Basic metric geometry of the bottleneck distance.
Manifolds that admit a double disk-bundle decomposition (2023)
Journal Article
DeVito, J., Galaz-García, F., & Kerin, M. (2023). Manifolds that admit a double disk-bundle decomposition. Indiana University Mathematics Journal, 72(4), 1503-1551. https://doi.org/10.1512/iumj.2023.72.9408
Cohomogeneity one manifolds and homogeneous spaces of positive scalar curvature (2022)
Journal Article
Frenck, G., Galaz‐García, F., & Reiser, P. (2022). Cohomogeneity one manifolds and homogeneous spaces of positive scalar curvature. Bulletin of the London Mathematical Society, 54(1), 71-82. https://doi.org/10.1112/blms.12557We characterize cohomogeneity one manifolds and homogeneous spaces with a compact Lie group action admitting an invariant metric with positive scalar curvature.
Stability of the cut locus and a Central Limit Theorem for Fréchet means of Riemannian manifolds (2021)
Journal Article
Eltzner, B., Galaz-García, F., Huckemann, S. F., & Tuschmann, W. (2021). Stability of the cut locus and a Central Limit Theorem for Fréchet means of Riemannian manifolds. Proceedings of the American Mathematical Society, 149(9), 3947-3963. https://doi.org/10.1090/proc/15429We obtain a central limit theorem for closed Riemannian manifolds, clarifying along the way the geometric meaning of some of the hypotheses in Bhattacharya and Lin’s Omnibus central limit theorem for Fréchet means. We obtain our CLT assuming certain... Read More about Stability of the cut locus and a Central Limit Theorem for Fréchet means of Riemannian manifolds.
Sufficiently collapsed irreducible Alexandrov 3-spaces are geometric (2020)
Journal Article
Galaz-García, F., Guijarro, L., & Núñez-Zimbrón, J. (2020). Sufficiently collapsed irreducible Alexandrov 3-spaces are geometric. Indiana University Mathematics Journal, 69(3), 977-1005. https://doi.org/10.1512/iumj.2020.69.7879
Cohomogeneity one Alexandrov spaces in low dimensions (2020)
Journal Article
Galaz-García, F., & Zarei, M. (2020). Cohomogeneity one Alexandrov spaces in low dimensions. Annals of Global Analysis and Geometry, 58(2), 109-146. https://doi.org/10.1007/s10455-020-09716-7Alexandrov spaces are complete length spaces with a lower curvature bound in the triangle comparison sense. When they are equipped with an effective isometric action of a compact Lie group with one-dimensional orbit space, they are said to be of coho... Read More about Cohomogeneity one Alexandrov spaces in low dimensions.
Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions (2020)
Journal Article
Corro, D., & Galaz-García, F. (2020). Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions. Proceedings of the American Mathematical Society, 148(7), 3087-3097. https://doi.org/10.1090/proc/14961We show that for each n 1, there exist infinitely many spin and non-spin diffeomorphism types of closed, smooth, simply-connected (n + 4)- manifolds with a smooth, effective action of a torus T n+2 and a metric of positive Ricci curvature invariant u... Read More about Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions.
Torus actions on rationally elliptic manifolds (2020)
Journal Article
Galaz-García, F., Kerin, M., & Radeschi, M. (2021). Torus actions on rationally elliptic manifolds. Mathematische Zeitschrift, 297, 197-221. https://doi.org/10.1007/s00209-020-02508-6An upper bound is obtained on the rank of a torus which can act smoothly and effectively on a smooth, closed (simply connected) rationally elliptic manifold. In the maximal-rank case, the manifolds admitting such actions are classified up to equivari... Read More about Torus actions on rationally elliptic manifolds.
Three-dimensional Alexandrov spaces with local isometric circle actions (2020)
Journal Article
Galaz-García, F., & Núñez-Zimbrón, J. (2020). Three-dimensional Alexandrov spaces with local isometric circle actions. Kyoto journal of mathematics, 60(3), 801-823. https://doi.org/10.1215/21562261-2019-0047
Finiteness and realization theorems for Alexandrov spaces with bounded curvature (2019)
Journal Article
Galaz-García, F., & Tuschmann, W. (2020). Finiteness and realization theorems for Alexandrov spaces with bounded curvature. Boletín de la Sociedad Matemática Mexicana, 26(2), 749-756. https://doi.org/10.1007/s40590-019-00262-2
On quotients of spaces with Ricci curvature bounded below (2018)
Journal Article
Galaz-García, F., Kell, M., Mondino, A., & Sosa, G. (2018). On quotients of spaces with Ricci curvature bounded below. Journal of Functional Analysis, 275(6), 1368-1446. https://doi.org/10.1016/j.jfa.2018.06.002
Cohomogeneity one topological manifolds revisited (2017)
Journal Article
Galaz-García, F., & Zarei, M. (2018). Cohomogeneity one topological manifolds revisited. Mathematische Zeitschrift, 288(3-4), 829-853. https://doi.org/10.1007/s00209-017-1915-yWe prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the equivariant classification of closed, simply-connected cohomogeneity one topological manifolds in... Read More about Cohomogeneity one topological manifolds revisited.
Three-Dimensional Alexandrov Spaces with Positive or Nonnegative Ricci Curvature (2017)
Journal Article
Deng, Q., Galaz-García, F., Guijarro, L., & Munn, M. (2018). Three-Dimensional Alexandrov Spaces with Positive or Nonnegative Ricci Curvature. Potential Analysis, 48(2), 223-238. https://doi.org/10.1007/s11118-017-9633-y
Torus Orbifolds, Slice-Maximal Torus Actions, and Rational Ellipticity (2017)
Journal Article
Galaz-García, F., Kerin, M., Radeschi, M., & Wiemeler, M. (2018). Torus Orbifolds, Slice-Maximal Torus Actions, and Rational Ellipticity. International Mathematics Research Notices, 2018(18), 5786-5822. https://doi.org/10.1093/imrn/rnx064In this work, it is shown that a simply connected, rationally elliptic torus orbifold is equivariantly rationally homotopy equivalent to the quotient of a product of spheres by an almost-free, linear torus action, where this torus has rank equal to t... Read More about Torus Orbifolds, Slice-Maximal Torus Actions, and Rational Ellipticity.
A glance at three-dimensional Alexandrov spaces (2016)
Journal Article
Galaz-García, F. (2016). A glance at three-dimensional Alexandrov spaces. Frontiers of Mathematics in China, 11(5), 1189-1206. https://doi.org/10.1007/s11464-016-0582-3
Singular Riemannian foliations and applications to positive and non-negative curvature (2015)
Journal Article
Galaz-Garcia, F., & Radeschi, M. (2015). Singular Riemannian foliations and applications to positive and non-negative curvature. Journal of Topology, 8(3), 603-620. https://doi.org/10.1112/jtopol/jtv004
Every point in a Riemannian manifold is critical (2015)
Journal Article
Galaz-García, F., & Guijarro, L. (2015). Every point in a Riemannian manifold is critical. Calculus of Variations and Partial Differential Equations, 54(2), 2079-2084. https://doi.org/10.1007/s00526-015-0857-7
Nonnegatively curved 5–manifolds with almost maximal symmetry rank (2014)
Journal Article
Galaz-Garcia, F., & Searle, C. (2014). Nonnegatively curved 5–manifolds with almost maximal symmetry rank. Geometry & Topology, 18(3), 1397-1435. https://doi.org/10.2140/gt.2014.18.1397