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pro vyhledávání: '"KETTERER, CHRISTIAN"'
Autor:
Ketterer, Christian
In this short note we survey theorems and provide conjectures on gluing constructions under lower curvature bounds in smooth and non-smooth context. Focusing on synthetic lower Ricci curvature bounds we consider Riemannian manifolds, weighted Riemann
Externí odkaz:
http://arxiv.org/abs/2408.13137
We establish a nonlinear analogue of a splitting map into a Euclidean space, as a harmonic map into a flat torus. We prove that the existence of such a map implies Gromov-Hausdorff closeness to a flat torus in any dimension. Furthermore, Gromov-Hausd
Externí odkaz:
http://arxiv.org/abs/2311.01342
Autor:
Ketterer, Christian
We consider Riemannian manifolds $M_i$, ${i=0,1}$, with boundary and $\Phi_i\in C^{\infty}(M_i)$ non-negative such that the pair $(M_i, \Phi_i)$ admits Bakry-Emery $N$-Ricci curvature bounded from below by $K$. Let $Y_0$ and $Y_1$ be isometric, compa
Externí odkaz:
http://arxiv.org/abs/2308.06848
Autor:
Ketterer, Christian
We characterize the null energy condition for an $(n+1)$-dimensional Lorentzian manifold in terms of convexity of the relative $(n-1)$-Renyi entropy along displacement interpolations on null hypersurfaces. More generally, we also consider Lorentzian
Externí odkaz:
http://arxiv.org/abs/2304.01853
Autor:
Ketterer, Christian
We prove splitting theorems for mean convex open subsets in RCD (Riemannian curvature-dimension) spaces that extend results by Kasue, Croke and Kleiner for Riemannian manifolds with boundary to a non-smooth setting. A corollary is for instance Franke
Externí odkaz:
http://arxiv.org/abs/2111.12020
Publikováno v:
Nonlinear Analysis 228 (2023)
We extend the celebrated rigidity of the sharp first spectral gap under $Ric\ge0$ to compact infinitesimally Hilbertian spaces with non-negative (weak, also called synthetic) Ricci curvature and bounded (synthetic) dimension i.e. to so-called compact
Externí odkaz:
http://arxiv.org/abs/2110.05045
Autor:
Ketterer, Christian
In this article we study stability and compactness w.r.t. measured Gromov-Hausdorff convergence of smooth metric measure spaces with integral Ricci curvature bounds. More precisely, we prove that a sequence of $n$-dimensional Riemannian manifolds sub
Externí odkaz:
http://arxiv.org/abs/2006.09458
Publikováno v:
SIGMA 16 (2020), 131, 29 pages
Consider an essentially nonbranching metric measure space with the measure contraction property of Ohta and Sturm, or with a Ricci curvature lower bound in the sense of Lott, Sturm and Villani. We prove a sharp upper bound on the inscribed radius of
Externí odkaz:
http://arxiv.org/abs/2005.07435
In this paper we prove that in the class of metric measure spaces with Alexandrov curvature bounded from below the Riemannian curvature-dimension condition $RCD(K,N)$ with $K\in \mathbb{R}$ and $N\in [1,\infty)$ is preserved under doubling and gluing
Externí odkaz:
http://arxiv.org/abs/2003.06242
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