27 citations · 87 across the 21 of their papers we have counts for
28 papers
Positive sectional curvature on exotic spheres in infinitely many dimensions
Fernando Galaz-García
We show that there exist exotic spheres with metrics of strictly positive sectional curvature in infinitely many dimensions: in every dimension with and…
Positive sectional curvature on the exotic -sphere and order-three homotopy -spheres
Fernando Galaz-García
We prove that the exotic smooth -sphere and both oriented homotopy -spheres representing elements of order three admit Riemannian metrics with strictly positive sectional cu…
Classification of generalized Seifert fiber spaces
Fernando Galaz-Garcia, Jesús Núñez-Zimbrón
We provide a symbolic classification of generalized Seifert fiber spaces, which were introduced by Mitsuishi and Yamaguchi in the classification of collapsing Alexandrov -spaces…
Wrapped Distributions on homogeneous Riemannian manifolds
Fernando Galaz-Garcia, Marios Papamichalis, Kathryn Turnbull +2
We provide a general framework for constructing probability distributions on Riemannian manifolds, taking advantage of area-preserving maps and isometries. Control over distributio…
Kurdyka-Łojasiewicz functions and mapping cylinder neighborhoods
Florentiu Daniel Cibotaru, Fernando Galaz-Garcia
Kurdyka-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,…
Cohomogeneity One Manifolds and Homogeneous Spaces of Positive Scalar Curvature
Georg Frenck, Fernando Galaz-Garcia, Philipp Reiser
We characterize cohomogeneity one manifolds and homogeneous spaces with a compact Lie group action admitting an invariant metric with positive scalar curvature.
Manifolds that admit a double disk-bundle decomposition
Jason DeVito, Fernando Galaz-Garcia, Martin Kerin
Under mild topological restrictions, this article establishes that a smooth, closed, simply connected manifold of dimension at most seven which can be decomposed as the union of tw…
Stability of the Cut Locus and a Central Limit Theorem for Fréchet Means of Riemannian Manifolds
Benjamin Eltzner, Fernando Galaz-Garcia, Stephan F. Huckemann +1
We 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 Centra…
Cohomogeneity one Alexandrov spaces in low dimensions
Fernando Galaz-Garcia, Masoumeh Zarei
We classify closed, simply-connected cohomogeneity-one Alexandrov spaces in dimensions , and . We show that every closed, simply-connected smooth -orbifold, $2\leq n\l…
Sufficiently collapsed irreducible Alexandrov 3-spaces are geometric
Fernando Galaz-Garcia, Luis Guijarro, Jesús Núñez-Zimbrón
We prove that sufficiently collapsed, closed and irreducible three-dimensional Alexandrov spaces are modeled on one of the eight three-dimensional Thurston geometries. This extends…
Three-dimensional Alexandrov spaces with local isometric circle actions
Fernando Galaz-Garcia, Jesús Núñez-Zimbrón
We obtain a topological and equivariant classification of closed, connected three-dimensional Alexandrov spaces admitting a local isometric circle action. We show, in particular, t…
Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions
Diego Corro, Fernando Galaz-Garcia
A gap in the proof of the main result in reference [1] in our original submission propagated into the constructions presented in the first version of our manuscript. In this versio…
Three-Dimensional Alexandrov spaces with positive or nonnegative Ricci curvature
Qintao Deng, Fernando Galaz-Garcia, Luis Guijarro +1
We study closed three-dimensional Alexandrov spaces with a lower Ricci curvature bound in the sense, focusing our attention on those with positive or nonnegati…
Torus actions on rationally elliptic manifolds
Fernando Galaz-Garcia, Martin Kerin, Marco Radeschi
An 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 ca…
Cohomogeneity one topological manifolds revisited
Fernando Galaz-Garcia, Masoumeh Zarei
We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the equivariant classification…
Every point in a Riemmanian manifold is critical
Fernando Galaz-Garcia, Luis Guijarro
We show that for any point in a closed Riemannian manifold , there exists at least one point such that is critical for the distance function from . We also s…
Torus orbifolds, slice-maximal torus actions and rational ellipticity
Fernando Galaz-Garcia, Martin Kerin, Marco Radeschi +1
In 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…
On three-dimensional Alexandrov spaces
Fernando Galaz-Garcia, Luis Guijarro
We study three-dimensional Alexandrov spaces with a lower curvature bound, focusing on extending three classical results on three-dimensional manifolds: First, we show that a close…
Singular Riemannian foliations and applications to positive and nonnegative curvature
Fernando Galaz-Garcia, Marco Radeschi
We determine the structure of the fundamental group of the regular leaves of a closed singular Riemannian foliation on a compact, simply connected Riemannian manifold. We also stud…
Simply connected Alexandrov 4-manifolds with positive or nonnegative curvature and torus actions
Fernando Galaz-Garcia
We point out that a 4-dimensional topological manifold with an Alexandrov metric (of curvature bounded below) and with an effective, isometric action of the circle or the 2-torus i…
Low-dimensional manifolds with non-negative curvature and maximal symmetry rank
Fernando Galaz-Garcia, Catherine Searle
We classify closed, simply connected -manifolds of non-negative sectional curvature admitting an isometric torus action of maximal symmetry rank in dimensions . I…
A note on maximal symmetry rank, quasipositive curvature, and low dimensional manifolds
Fernando Galaz-Garcia
We show that any effective isometric torus action of maximal rank on a compact Riemannian manifold with positive (sectional) curvature and maximal symmetry rank, that is, on a posi…
Cohomogeneity-two torus actions on non-negatively curved manifolds of low dimension
Fernando Galaz-Garcia, Martin Kerin
Let , , be a compact, simply connected -manifold which admits some Riemannian metric with non-negative curvature and an isometry group of maximal possible…
Isometry groups of Alexandrov spaces
Fernando Galaz-Garcia, Luis Guijarro
For an Alexandrov space (with curvature bounded below), we determine the maximal dimension of its isometry group and show that the space is isometric to a Riemannian manifold, prov…