21 citations · 73 across the 24 of their papers we have counts for
16 papers · 1 filter
Upper and lower bounds on the filling radius
Manuel Cuerno, Luis Guijarro
We give a curvature dependent lower bound for the filling radius of all closed Riemannian manifolds as well as an upper one for manifolds which are the total space of a Riemannian…
Bounded distance geodesic foliations in Riemannian planes
Jian Ge, Luis Guijarro
A conjecture of Burns and Knieper asks whether a 2-plane with a metric without conjugate points, and with a geodesic foliation whose lines are at bounded Hausdorff distance, is nec…
A softer connectivity principle
Luis Guijarro, Frederick Wilhelm
We give soft, quantitatively optimal extensions of the classical Sphere Theorem, Wilking's connectivity principle and Frankel's Theorem to the context of -th Ricci curvature.…
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…
Riemannian Rigidity of the Parallel Postulate in Total Curvature
Jian Ge, Luis Guijarro, Pedro Solórzano
We prove that the Euclidean plane is the only Riemannian plane with total curvature and free of conjugate points that satisfies Playfair's version of the parallel postulate.
On the isometry group of -spaces
Luis Guijarro, Jaime Santos-Rodríguez
We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition, is in fact a Lie group. We obtain an optimal upper…