Non-Hilbertian tangents to Hilbertian spaces

DOI10.1017/prm.2022.18arXiv2111.06777MaRDI QIDQ6111243

Enrico Pasqualetto, Tapio Rajala, Danka Lučić

Publication date: 6 July 2023

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.06777

zbMATH Keywords

tangent coneinfinitesimal HilbertianityPI space

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Lipschitz and coarse geometry of metric spaces (51F30)

Cites Work

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• The Lip-lip equality is stable under blow-up
• Infinitesimal structure of differentiability spaces, and metric differentiation
• Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
• Local Poincaré inequalities from stable curvature conditions on metric spaces
• Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below
• Nonlinear potential theory on metric spaces
• On the limits of periodic Riemannian metrics
• Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• Relative volume comparison with integral curvature bounds
• Characterizing spaces satisfying Poincaré inequalities and applications to differentiability
• A differentiable structure for metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Stability of metric measure spaces with integral Ricci curvature bounds
• Behaviour of the reference measure on \(\mathsf{RCD}\) spaces under charts
• Gamma-convergence of Cheeger energies with respect to increasing distances
• Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces
• Korevaar-Schoen's energy on strongly rectifiable spaces
• Structure theory of metric measure spaces with lower Ricci curvature bounds
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• On the geometry of metric measure spaces. II
• On the differential structure of metric measure spaces and applications
• Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
• Rectifiable Metric Spaces: Local Structure and Regularity of the Hausdorff Measure
• On the volume measure of non-smooth spaces with Ricci curvature bounded below
• Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below
• Measurable differentiable structures and the Poincare inequality
• On a conjecture of Cheeger
• Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows
• CALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACES
• Abstract and concrete tangent modules on Lipschitz differentiability spaces
• Sobolev Spaces on Metric Measure Spaces
• Infinitesimal Hilbertianity of Weighted Riemannian Manifolds
• Finiteness of π1π1 and geometric inequalities in almost positive Ricci curvature
• Structure of measures in Lipschitz differentiability spaces

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