Fernando Galaz-García

activity

20092026

most citedTorus orbifolds, slice-maximal torus actions and rational ellipticity

27 citations · 87 across the 21 of their papers we have counts for

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24 papers · 1 filter

math.DG2026

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 $n \equiv 3 (mod 4)$ with $n \geq 11$ and…

math.DG2026

Positive sectional curvature on the exotic $8$ -sphere and order-three homotopy $10$ -spheres

Fernando Galaz-García

We prove that the exotic smooth $8$ -sphere and both oriented homotopy $10$ -spheres representing elements of order three admit Riemannian metrics with strictly positive sectional cu…

math.DG2020

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.

math.DG2020★ 1 cited

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…

math.DG2019

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…

math.DG2017

Cohomogeneity one Alexandrov spaces in low dimensions

Fernando Galaz-Garcia, Masoumeh Zarei

We classify closed, simply-connected cohomogeneity-one Alexandrov spaces in dimensions $5$ , $6$ and $7$ . We show that every closed, simply-connected smooth $n$ -orbifold, $2\leq n\l…

math.DG2017★ 4 cited

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…

math.DG2017★ 5 cited

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…

math.DG2016★ 2 cited

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…

math.DG2016★ 1 cited

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 $CD^{*} (K, N)$ sense, focusing our attention on those with positive or nonnegati…

math.DG2015

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…

math.DG2014

Every point in a Riemmanian manifold is critical

Fernando Galaz-Garcia, Luis Guijarro

We show that for any point $p$ in a closed Riemannian manifold $M$ , there exists at least one point $q \in M$ such that $p$ is critical for the distance function from $q$ . We also s…

math.DG2014★ 27 cited

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…

math.DG2013

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…

math.DG2013★ 17 cited

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…

math.DG2012★ 2 cited

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…

math.DG2012

Low-dimensional manifolds with non-negative curvature and maximal symmetry rank

Fernando Galaz-Garcia, Catherine Searle

We classify closed, simply connected $n$ -manifolds of non-negative sectional curvature admitting an isometric torus action of maximal symmetry rank in dimensions $2 \leq n \leq 6$ . I…

math.DG2012★ 1 cited

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…

math.DG2011★ 1 cited

Cohomogeneity-two torus actions on non-negatively curved manifolds of low dimension

Fernando Galaz-Garcia, Martin Kerin

Let $M^{n}$ , $n \in {4, 5, 6}$ , be a compact, simply connected $n$ -manifold which admits some Riemannian metric with non-negative curvature and an isometry group of maximal possible…

math.DG2011★ 21 cited

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…

math.DG2011

Nonnegatively curved fixed point homogeneous 5-manifolds

Fernando Galaz-Garcia, Wolfgang Spindeler

Let $G$ be a compact Lie group acting effectively by isometries on a compact Riemannian manifold $M$ with nonempty fixed point set $F i x (M, G)$ . We say that the action is \emph{fixed…

math.DG2009★ 1 cited

Nonnegatively curved fixed point homogeneous manifolds in low dimensions

Fernando Galaz-Garcia

Let $G$ be a compact Lie group acting isometrically on a compact Riemannian manifold $M$ with nonempty fixed point set $M^{G}$ . We say that $M$ is fixed-point homogeneous if $G$ acts…

math.DG2009

Cohomogeneity One Alexandrov Spaces

Fernando Galaz-Garcia, Catherine Searle

We obtain a structure theorem for closed, cohomogeneity one Alexandrov spaces and we classify closed, cohomogeneity one Alexandrov spaces in dimensions 3 and 4. As a corollary, we…

math.DG2009★ 3 cited

Non-negatively Curved Manifolds with Maximal Symmetry Rank in Low Dimensions

Fernando Galaz-Garcia, Catherine Searle

We classify closed, simply-connected non-negatively curved 5-manifolds admitting an (almost) effective, isometric $T^{3}$ or $T^{2}$ action. As a direct consequence, we show that for a…

Positive sectional curvature on exotic spheres in infinitely many dimensions

Positive sectional curvature on the exotic 8-sphere and order-three homotopy 10-spheres

Cohomogeneity One Manifolds and Homogeneous Spaces of Positive Scalar Curvature

Manifolds that admit a double disk-bundle decomposition

Stability of the Cut Locus and a Central Limit Theorem for Fréchet Means of Riemannian Manifolds

Cohomogeneity one Alexandrov spaces in low dimensions

Sufficiently collapsed irreducible Alexandrov 3-spaces are geometric

Three-dimensional Alexandrov spaces with local isometric circle actions

Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions

Three-Dimensional Alexandrov spaces with positive or nonnegative Ricci curvature

Torus actions on rationally elliptic manifolds

Every point in a Riemmanian manifold is critical

Torus orbifolds, slice-maximal torus actions and rational ellipticity

On three-dimensional Alexandrov spaces

Singular Riemannian foliations and applications to positive and nonnegative curvature

Simply connected Alexandrov 4-manifolds with positive or nonnegative curvature and torus actions

Low-dimensional manifolds with non-negative curvature and maximal symmetry rank

A note on maximal symmetry rank, quasipositive curvature, and low dimensional manifolds

Cohomogeneity-two torus actions on non-negatively curved manifolds of low dimension

Isometry groups of Alexandrov spaces

Nonnegatively curved fixed point homogeneous 5-manifolds

Nonnegatively curved fixed point homogeneous manifolds in low dimensions

Cohomogeneity One Alexandrov Spaces

Non-negatively Curved Manifolds with Maximal Symmetry Rank in Low Dimensions

Positive sectional curvature on the exotic $8$ -sphere and order-three homotopy $10$ -spheres