16 citations · 20 across the 7 of their papers we have counts for
11 papers
Balancing the 2-systoles of some Kähler manifolds with positive scalar curvature
Thomas Richard, Hugues Auvray
Theorems by Bray-Brendle-Neves and Zhu about positive scalar curvature metrics on products of a 2-sphere and an n-torus suggests that positive scalar curvature suggests and appropr…
Strengthened injectivity radius bounds for manifolds with positive scalar curvature
Thomas Richard
Green's inequality shows that a compact Riemannian manifold with scalar curvature at least has injectivity radius at most , and that equality is achieved only for the r…
Multi-resolution deep learning pipeline for dense large scale point clouds
Thomas Richard, Florent Dupont, Guillaume Lavoue
Recent development of 3D sensors allows the acquisition of extremely dense 3D point clouds of large-scale scenes. The main challenge of processing such large point clouds remains i…
On the 2-systole of stretched enough positive scalar curvature metrics on S 2 x S 2
Thomas Richard
We use recent developments by Gromov and Zhu to derive an upper bound for the 2-systole of the homology class of S 2 x { * } in a S 2 x S 2 with a positive scalar curvature metric…
Stratified spaces and synthetic Ricci curvature bounds
J. Bertrand, C Ketterer, Ilaria Mondello +1
We prove that a compact stratied space satises the Riemannian curvature-dimension condition RCD(K, N) if and only if its Ricci tensor is bounded below by K R on the regular s…
Stability of nonnegative isotropic curvature under continuous deformations of the metric
Thomas Richard
Using a method introduced by R. Bamler to study the behavior of scalar curvature under continuous deformations of Riemannian metrics, we prove that if a sequence of smooth Riemanni…
Curvature cones and the Ricci flow
Thomas Richard
This survey reviews some facts about nonnegativity conditions on the curvature tensor of a Riemannian manifold which are preserved by the action of the Ricci flow. The text focuses…
Positive isotropic curvature and self-duality in dimension 4
Thomas Richard, Harish Seshadri
We study a positivity condition for the curvature of oriented Riemannian 4-manifolds: The half- condition. It is a slight weakening of the positive isotropic curvature ()…
Noncoercive Ricci flow invariant curvature cones
Thomas Richard, Harish Seshadri
This note is a study of nonnegativity conditions on curvature which are preserved by the Ricci flow. We focus on specific kinds of curvature conditions which we call noncoercive, t…
Canonical smoothing of compact Alexandrov surfaces via Ricci flow
Thomas Richard
In this paper, we show existence and uniqueness of Ricci flow whose initial condition is a compact Alexandrov surface with curvature bounded from below. This requires a weakening o…
Lower bounds on Ricci flow invariant curvatures and geometric applications
Thomas Richard
We consider Ricci flow invariant cones C in the space of curvature operators lying between nonnegative Ricci curvature and nonnegative curvature operator. Assuming some mild contro…