Singular Weyl's law with Ricci curvature bounded below
We establish two surprising types of Weyl's laws for some compact $\operatorname
{RCD}(K, N) $/Ricci limit spaces. The first type could have power growth of any order (bigger …
{RCD}(K, N) $/Ricci limit spaces. The first type could have power growth of any order (bigger …
Remarks on manifolds with two-sided curvature bounds
V Kapovitch, A Lytchak - Analysis and Geometry in Metric Spaces, 2021 - degruyter.com
Remarks on Manifolds with Two-Sided Curvature Bounds Page 1 Open Access. © 2021 Vitali
Kapovitch and Alexander Lytchak, published by De Gruyter. This work is licensed under the …
Kapovitch and Alexander Lytchak, published by De Gruyter. This work is licensed under the …
[HTML][HTML] Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifolds
BX Han - Advances in Mathematics, 2020 - Elsevier
In this paper we investigate Lott-Sturm-Villani's synthetic lower Ricci curvature bound on
Riemannian manifolds with boundary. We prove several measure rigidity results related to …
Riemannian manifolds with boundary. We prove several measure rigidity results related to …
On the non-collapsed RCD spaces with local bounded covering geometry
J Wang - arXiv preprint arXiv:2412.06131, 2024 - arxiv.org
We consider a RCD $(-(N-1), N) $ space $(X, d,\mathcal {H}^ N) $ with local bounded
covering geometry. The first result is related to Gromov's almost flat manifold theorem …
covering geometry. The first result is related to Gromov's almost flat manifold theorem …
Stability of metric measure spaces with integral Ricci curvature bounds
C Ketterer - Journal of Functional Analysis, 2021 - Elsevier
In this article we study stability and compactness wrt measured Gromov-Hausdorff
convergence of smooth metric measure spaces with integral Ricci curvature bounds. More …
convergence of smooth metric measure spaces with integral Ricci curvature bounds. More …
Convergence and collapsing of CAT-lattices
N Cavallucci, A Sambusetti - arXiv preprint arXiv:2405.01595, 2024 - arxiv.org
We study the theory of convergence for CAT $(0) $-lattices (that is groups $\Gamma $ acting
geometrically on proper, geodesically complete CAT $(0) $-spaces) and their quotients …
geometrically on proper, geodesically complete CAT $(0) $-spaces) and their quotients …
Failure of strong unique continuation for harmonic functions on RCD Spaces
Q Deng, X Zhao - Journal für die reine und angewandte Mathematik …, 2023 - degruyter.com
Unique continuation of harmonic functions on RCD space is a long-standing open problem,
with little known even in the setting of Alexandrov spaces. In this paper, we establish the …
with little known even in the setting of Alexandrov spaces. In this paper, we establish the …
Glued spaces and lower curvature bounds
C Ketterer - arXiv preprint arXiv:2408.13137, 2024 - arxiv.org
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 …
lower curvature bounds in smooth and non-smooth context. Focusing on synthetic lower …
Glued spaces and lower Ricci curvature bounds
C Ketterer - arXiv preprint arXiv:2308.06848, 2023 - arxiv.org
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 …
C^{\infty}(M_i) $ non-negative such that the pair $(M_i,\Phi_i) $ admits Bakry-Emery $ N …
Mixed curvature almost flat manifolds
V Kapovitch - Geometry & Topology, 2021 - msp.org
A celebrated Almost Flat Manifolds Theorem of Gromov [22] says that for any natural number
n there exists a constant". n/such that if a closed manifold M n admits a Riemannian metric of …
n there exists a constant". n/such that if a closed manifold M n admits a Riemannian metric of …