Raquel Perales
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Raquel Perales has a total of 29 co-authors. Here are the top co-authors by number of shared publications:
- Jesús Núñez-Zimbrón
Universidad Nacional Autónoma de México
4 shared publications - Christian Ketterer
University of Toronto
3 shared publications - Armando J. Cabrera Pacheco
Department of Mathematics, Universität Tübingen, Tübingen, Germany
2 shared publications - Armando J. Cabrera Pacheco
Department of Mathematics, Universität Tübingen, Tübingen, Germany
2 shared publications - Brian Allen
Lehman College, CUNY, Bronx, USA
2 shared publications - Dan A. Lee
CUNY Graduate Center and Queens College, New York, USA
2 shared publications
Latest Publications
- Open Access
- 15 May 2026
- Published by Springer Nature in Boletín de la Sociedad Matemática Mexicana
- Vol. 32 (2)
Intrinsic timed-Hausdorff convergence and its implications
Sakovich–Sormani introduced several notions of distance between certain classes of Lorentzian manifolds. These distances use the Hausdorff and Gromov–Hausdorff distances and, therefore, extend naturally to a broader class of spaces. Here we show that, for timed-metric-spaces, intrinsic timed–Hausdorff convergence implies (timeless) Gromov–Hausdorff convergence as well as big bang convergence, among other related implications for future-developed convergence.
- 15 May 2026
- Published by Springer Nature in Boletín de la Sociedad Matemática Mexicana
- Vol. 32 (2)
Open AccessIntrinsic timed-Hausdorff convergence and its implications
Sakovich–Sormani introduced several notions of distance between certain classes of Lorentzian manifolds. These distances use the Hausdorff and Gromov–Hausdorff distances and, therefore, extend naturally to a broader class of spaces. Here we show that, for timed-metric-spaces, intrinsic timed–Hausdorff convergence implies (timeless) Gromov–Hausdorff convergence as well as big bang convergence, among other related implications for future-developed convergence.
- Open Access
Volume entropy and rigidity for RCD-spaces
We develop the barycenter technique of Besson--Courtois--Gallot so that it can be applied on RCD metric measure spaces. Given a continuous map $f$ from a non-collapsed RCD$(-(N-1),N)$ space $X$ without boundary to a locally symmetric $N$-manifold we show a version of BCG's entropy-volume inequality. The lower bound involves homological and homotopical indices which we introduce. We prove that when equality holds and these indices coincide $X$ is a locally symmetric manifold, and $f$ is homotopic to a Riemannian covering whose degree equals the indices. Moreover, we show a measured Gromov--Hausdorff stability of $X$ and $Y$ involving the homotopical invariant. As a byproduct, we extend a Lipschitz volume rigidity result of Li--Wang to RCD$(K,N)$ spaces without boundary. Finally, we include an application of these methods to the study of Einstein metrics on $4$-orbifolds.Open AccessVolume entropy and rigidity for RCD-spaces
We develop the barycenter technique of Besson--Courtois--Gallot so that it can be applied on RCD metric measure spaces. Given a continuous map $f$ from a non-collapsed RCD$(-(N-1),N)$ space $X$ without boundary to a locally symmetric $N$-manifold we show a version of BCG's entropy-volume inequality. The lower bound involves homological and homotopical indices which we introduce. We prove that when equality holds and these indices coincide $X$ is a locally symmetric manifold, and $f$ is homotopic to a Riemannian covering whose degree equals the indices. Moreover, we show a measured Gromov--Hausdorff stability of $X$ and $Y$ involving the homotopical invariant. As a byproduct, we extend a Lipschitz volume rigidity result of Li--Wang to RCD$(K,N)$ spaces without boundary. Finally, we include an application of these methods to the study of Einstein metrics on $4$-orbifolds. - Open Access
- 12 August 2024
- Published by Elsevier in Nonlinear Analysis
- Vol. 249
Gromov–Hausdorff stability of tori under Ricci and integral scalar curvature bounds
- 12 August 2024
- Published by Elsevier in Nonlinear Analysis
- Vol. 249
Open AccessGromov–Hausdorff stability of tori under Ricci and integral scalar curvature bounds
- 11 April 2024
- Published by Springer Nature in Boletín de la Sociedad Matemática Mexicana
- Vol. 30 (2) , 1-22
The mean curvature flow on solvmanifolds
- 11 April 2024
- Published by Springer Nature in Boletín de la Sociedad Matemática Mexicana
- Vol. 30 (2) , 1-22
The mean curvature flow on solvmanifolds
- Open Access
The mean curvature flow on solvmanifolds
This work is a survey of the most relevant background material to motivate and understand the construction and classification of translating solutions to mean curvature flow on a family of solvmanifolds. We introduce the mean curvature flow and some known results in the field. In particular we explore the notion of translating solution in the Euclidean space and extensions into other Riemannian manifolds. We also include a discussion on solvmanifolds and some elements of its geometry that are relevant to our work. We finish by posing the equations that describe translating solutions to mean curvature flow on our family of 3-dimensional solvmanifolds with some additional assumptions. This project emerged at the ``Latin American and Caribbean Workshop on Mathematics and Gender'' held at Casa Matemática Oaxaca (CMO) from May 15-20, 2022.
Open AccessThe mean curvature flow on solvmanifolds
This work is a survey of the most relevant background material to motivate and understand the construction and classification of translating solutions to mean curvature flow on a family of solvmanifolds. We introduce the mean curvature flow and some known results in the field. In particular we explore the notion of translating solution in the Euclidean space and extensions into other Riemannian manifolds. We also include a discussion on solvmanifolds and some elements of its geometry that are relevant to our work. We finish by posing the equations that describe translating solutions to mean curvature flow on our family of 3-dimensional solvmanifolds with some additional assumptions. This project emerged at the ``Latin American and Caribbean Workshop on Mathematics and Gender'' held at Casa Matemática Oaxaca (CMO) from May 15-20, 2022.
- Open Access
- 13 November 2023
- Published by Springer Nature in General Relativity and Gravitation
- Vol. 55 (11) , 1-45
Intrinsic flat stability of the positive mass theorem for asymptotically hyperbolic graphical manifolds
The rigidity of the Riemannian positive mass theorem for asymptotically hyperbolic manifolds states that the total mass of such a manifold is zero if and only if the manifold is isometric to the hyperbolic space. This leads to study the stability of this statement, that is, if the total mass of an asymptotically hyperbolic manifold is almost zero, is this manifold close to the hyperbolic space in any way? Motivated by the work of Huang, Lee and Sormani for asymptotically flat graphical manifolds with respect to intrinsic flat distance, we show the intrinsic flat stability of the positive mass theorem for a class of asymptotically hyperbolic graphical manifolds by adapting the positive answer to this question provided by Huang, Lee and the third named author.
- 13 November 2023
- Published by Springer Nature in General Relativity and Gravitation
- Vol. 55 (11) , 1-45
Open AccessIntrinsic flat stability of the positive mass theorem for asymptotically hyperbolic graphical manifolds
The rigidity of the Riemannian positive mass theorem for asymptotically hyperbolic manifolds states that the total mass of such a manifold is zero if and only if the manifold is isometric to the hyperbolic space. This leads to study the stability of this statement, that is, if the total mass of an asymptotically hyperbolic manifold is almost zero, is this manifold close to the hyperbolic space in any way? Motivated by the work of Huang, Lee and Sormani for asymptotically flat graphical manifolds with respect to intrinsic flat distance, we show the intrinsic flat stability of the positive mass theorem for a class of asymptotically hyperbolic graphical manifolds by adapting the positive answer to this question provided by Huang, Lee and the third named author.
- Open Access
Intrinsic flat stability of the positive mass theorem for asymptotically hyperbolic graphical manifolds
The rigidity of the Riemannian positive mass theorem for asymptotically hyperbolic manifolds states that the total mass of such a manifold is zero if and only if the manifold is isometric to the hyperbolic space. This leads to study the stability of this statement, that is, if the total mass of an asymptotically hyperbolic manifold is almost zero, is this manifold close to the hyperbolic space in any way? Motivated by the work of Huang, Lee and Sormani for asymptotically flat graphical manifolds with respect to intrinsic flat distance, we show the intrinsic flat stability of the positive mass theorem for a class of asymptotically hyperbolic graphical manifolds by adapting the positive answer to this question provided by Huang, Lee and the third named author.
Open AccessIntrinsic flat stability of the positive mass theorem for asymptotically hyperbolic graphical manifolds
The rigidity of the Riemannian positive mass theorem for asymptotically hyperbolic manifolds states that the total mass of such a manifold is zero if and only if the manifold is isometric to the hyperbolic space. This leads to study the stability of this statement, that is, if the total mass of an asymptotically hyperbolic manifold is almost zero, is this manifold close to the hyperbolic space in any way? Motivated by the work of Huang, Lee and Sormani for asymptotically flat graphical manifolds with respect to intrinsic flat distance, we show the intrinsic flat stability of the positive mass theorem for a class of asymptotically hyperbolic graphical manifolds by adapting the positive answer to this question provided by Huang, Lee and the third named author.
- Open AccessRigidity of mass-preserving $1$-Lipschitz maps from integral current spaces into $\mathbb{R}^n$
We prove that given an $n$-dimensional integral current space and a $1$-Lipschitz map, from this space onto the $n$-dimensional Euclidean ball, that preserves the mass of the current and is injective on the boundary, then the map has to be an isometry. We deduce as a consequence a stability result with respect to the intrinsic flat distance, which implies the stability of the positive mass theorem for graphical manifolds as originally formulated by Huang--Lee--Sormani.
Open AccessRigidity of mass-preserving $1$-Lipschitz maps from integral current spaces into $\mathbb{R}^n$We prove that given an $n$-dimensional integral current space and a $1$-Lipschitz map, from this space onto the $n$-dimensional Euclidean ball, that preserves the mass of the current and is injective on the boundary, then the map has to be an isometry. We deduce as a consequence a stability result with respect to the intrinsic flat distance, which implies the stability of the positive mass theorem for graphical manifolds as originally formulated by Huang--Lee--Sormani.
- 9 November 2022
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 62 (1) , 1-34
Yamabe problem in the presence of singular Riemannian Foliations
- 9 November 2022
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 62 (1) , 1-34
Yamabe problem in the presence of singular Riemannian Foliations
- Open Access
Volume Above Distance Below
Given a pair of metric tensors $g_1 \ge g_0$ on a Riemannian manifold, $M$, it is well known that $\operatorname{Vol}_1(M) \ge \operatorname{Vol}_0(M)$. Furthermore one has rigidity: the volumes are equal if and only if the metric tensors are the same $g_1=g_0$. Here we prove that if $g_j \ge g_0$ and $\operatorname{Vol}_1(M)\to \operatorname{Vol}_0(M)$ then $(M,g_j)$ converge to $(M,g_0)$ in the volume preserving intrinsic flat sense. Well known examples demonstrate that one need not obtain smooth, $C^0$, Lipschitz, or even Gromov-Hausdorff convergence in this setting. Our theorem may also be applied as a tool towards proving other open conjectures concerning the geometric stability of a variety of rigidity theorems in Riemannian geometry. To complete our proof, we provide a novel way of estimating the intrinsic flat distance between Riemannian manifolds which is interesting in its own right.Open AccessVolume Above Distance Below
Given a pair of metric tensors $g_1 \ge g_0$ on a Riemannian manifold, $M$, it is well known that $\operatorname{Vol}_1(M) \ge \operatorname{Vol}_0(M)$. Furthermore one has rigidity: the volumes are equal if and only if the metric tensors are the same $g_1=g_0$. Here we prove that if $g_j \ge g_0$ and $\operatorname{Vol}_1(M)\to \operatorname{Vol}_0(M)$ then $(M,g_j)$ converge to $(M,g_0)$ in the volume preserving intrinsic flat sense. Well known examples demonstrate that one need not obtain smooth, $C^0$, Lipschitz, or even Gromov-Hausdorff convergence in this setting. Our theorem may also be applied as a tool towards proving other open conjectures concerning the geometric stability of a variety of rigidity theorems in Riemannian geometry. To complete our proof, we provide a novel way of estimating the intrinsic flat distance between Riemannian manifolds which is interesting in its own right.