Zobrazeno 1 - 10
of 257
pro vyhledávání: '"Mondino, Andrea"'
Autor:
Honda, Shouhei, Mondino, Andrea
In the paper we discuss gap phenomena of three different types related to Ricci (and sectional) curvature. The first type is about spectral gaps. The second type is about sharp gap metric-rigidity, originally due to Anderson. The third is about sharp
Externí odkaz:
http://arxiv.org/abs/2410.04985
Autor:
Kristály, Alexandru, Mondino, Andrea
We study fine properties of the principal frequency of clamped plates in the (possibly singular) setting of metric measure spaces verifying the RCD(0,N) condition, i.e., infinitesimally Hilbertian spaces with non-negative Ricci curvature and dimensio
Externí odkaz:
http://arxiv.org/abs/2409.04337
The goal of the present work is to study optimal transport on null hypersurfaces inside Lorentzian manifolds. The challenge here is that optimal transport along a null hypersurface is completely degenerate, as the cost takes only the two values $0$ a
Externí odkaz:
http://arxiv.org/abs/2408.08986
Autor:
Cucinotta, Alessandro, Mondino, Andrea
We prove a warped product splitting theorem for manifolds with Ricci curvature bounded from below in the spirit of [Croke-Kleiner, Duke Math. J. (1992)], but instead of asking that one boundary component is compact and mean convex, we require that it
Externí odkaz:
http://arxiv.org/abs/2406.09784
For the Laplacian of an $n$-Riemannian manifold $X$, the Weyl law states that the $k$-th eigenvalue is asymptotically proportional to $(k/V)^{2/n}$, where $V$ is the volume of $X$. We show that this result can be derived via physical considerations b
Externí odkaz:
http://arxiv.org/abs/2406.00095
Autor:
Honda, Shouhei, Mondino, Andrea
In this short note, we provide a quantitative global Poincar\'e inequality for one forms on a closed Riemannian four manifold, in terms of an upper bound on the diameter, a positive lower bound on the volume, and a two-sided bound on Ricci curvature.
Externí odkaz:
http://arxiv.org/abs/2405.19168
Autor:
Cucinotta, Alessandro, Mondino, Andrea
The goal of this note is to prove the Half Space Property for $RCD(0,N)$ spaces, namely that if $(X,d,m)$ is a parabolic $RCD(0,N)$ space and $ C \subset X \times \mathbb{R}$ is locally the boundary of a locally perimeter minimizing set and it is con
Externí odkaz:
http://arxiv.org/abs/2402.12230
Autor:
Mondino, Andrea, Ryborz, Vanessa
The goal of the paper is to prove the equivalence of distributional and synthetic Ricci curvature lower bounds for a weighted Riemannian manifold with continuous metric tensor having Christoffel symbols in $L^2_{{\rm loc}}$, and with weight in $C^0\c
Externí odkaz:
http://arxiv.org/abs/2402.06486
Autor:
Cavalletti, Fabio, Mondino, Andrea
The paper establishes a sharp and rigid isoperimetric-type inequality in Lorentzian signature under the assumption of Ricci curvature bounded below in the timelike directions. The inequality is proved in the high generality of Lorentzian pre-length s
Externí odkaz:
http://arxiv.org/abs/2401.03949
The goal of this paper is to establish a monotonicity formula for perimeter minimizing sets in RCD(0,N) metric measure cones, together with the associated rigidity statement. The applications include sharp Hausdorff dimension estimates for the singul
Externí odkaz:
http://arxiv.org/abs/2307.06205