10 citations · 48 across the 16 of their papers we have counts for
19 papers
Orientability of metric manifolds and metric spaces with curvature bounds
Nicola Cavallucci, Denis Marti, Andrea Mondino +1
We develop a theory of orientability for metric manifolds and singular metric spaces using locally integral currents. For topological -manifolds with locally finite Hausdorff me…
The mean curvature flow on solvmanifolds
Romina M. Arroyo, Gabriela P. Ovando, Raquel Perales +1
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 f…
Intrinsic flat stability of the positive mass theorem for asymptotically hyperbolic graphical manifolds
Armando J. Cabrera Pacheco, Melanie Graf, Raquel Perales
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 is…
Rigidity of mass-preserving -Lipschitz maps from integral current spaces into
Giacomo Del Nin, Raquel Perales
We prove that given an -dimensional integral current space and a -Lipschitz map, from this space onto the -dimensional Euclidean ball, that preserves the mass of the curre…
Semicontinuity of capacity under pointed intrinsic flat convergence
Jeffrey L. Jauregui, Raquel Perales, Jacobus W. Portegies
The concept of the capacity of a compact set in generalizes readily to noncompact Riemannian manifolds and, with more substantial work, to metric spaces (where multip…
Yamabe problem in the presence of singular Riemannian Foliations
Diego Corro, Juan Carlos Fernández, Raquel Perales
Using variational methods together with symmetries given by singular Riemannian foliations with positive dimensional leaves, we prove the existence of an infinite number of sign-ch…
An upper bound on the revised first Betti number and a torus stability result for RCD spaces
Ilaria Mondello, Andrea Mondino, Raquel Perales
We prove an upper bound on the rank of the abelianised revised fundamental group (called "revised first Betti number") of a compact space, in the same spirit of the…
Intrinsic flat convergence of points and applications to stability of the positive mass theorem
Lan-Hsuan Huang, Dan A. Lee, Raquel Perales
We prove results on intrinsic flat convergence of points---a concept first explored by Sormani in \cite{Sormani-AA}. In particular, we discuss compatibility with Gromov-Hausdorff c…
Intrinsic Flat Stability of Manifolds with Boundary where Volume Converges and Distance is Bounded Below
Brian Allen, Raquel Perales
Given a compact, connected, and oriented manifold with boundary and a sequence of smooth Riemannian metrics defined on it, , we prove volume preserving intrinsic flat conv…
Volume Above Distance Below
Brian Allen, Raquel Perales, Christina Sormani
Given a pair of metric tensors on a Riemannian manifold, , it is well known that . Furthermore one has rigidit…
Stability of graphical tori with almost nonnegative scalar curvature
Armando J. Cabrera Pacheco, Christian Ketterer, Raquel Perales
By works of Schoen-Yau and Gromov-Lawson any Riemannian manifold with nonnegative scalar curvature and diffeomorphic to a torus is isometric to a flat torus. Gromov conjectured sub…
Maximal volume entropy rigidity for spaces
Chris Connell, Xianzhe Dai, Jesús Núñez-Zimbrón +3
For -dimensional Riemannian manifolds with Ricci curvature bounded below by , the volume entropy is bounded above by . If is compact, it is known that the e…
A generalized tetrahedral property
Jesús Nuñez-Zimbrón, Raquel Perales
We present examples of metric spaces that are not Riemannian manifolds nor dimensionally homogeneous that satisfy the Tetrahedral Property. In spite of that, Euclidean cones over m…
Alexandrov Spaces with Integral Current Structure
Maree Jaramillo, Raquel Perales, Priyanka Rajan +2
We endow each closed, orientable Alexandrov space with an integral current of weight equal to 1, , in other words, we prove that $(X, d…
Convergence of Manifolds and Metric Spaces with Boundary
Raquel Perales
We study sequences of oriented Riemannian manifolds with boundary and, more generally, integral current spaces and metric spaces with boundary. {\color{blue}For a metric space, we…
On the Sormani-Wenger Intrinsic Flat Convergence of Alexandrov Spaces
Nan Li, Raquel Perales
We study sequences of integral current spaces such that the integral current structure has weight and no boundary and, all are closed Alexandr…
Volumes and Limits of Manifolds with Ricci Curvature and Mean Curvature Bounds
Raquel Perales
We prove a laplacian comparison theorem in the barrier sense for the function distance to the boundary of Riemannian manifolds with nonnegative Ricci curvature, area and mean curva…
A survey on the Convergence of Manifolds with Boundary
Raquel Perales
This survey reviews precompactness theorems for classes of Riemannian manifolds with boundary. We begin with the works of Kodani, Anderson-Katsuda-Kurylev-Lassas-Taylor and Wong. W…
Sequences of Open Riemannian Manifolds with Boundary
Raquel Perales, Christina Sormani
We consider sequences of open Riemannian manifolds with boundary that have no regularity conditions on the boundary. To define a reasonable notion of a limit of such a sequence, we…