Infinitesimal hilbertianity of locally \(\mathrm{CAT}(\kappa)\)-spaces

DOI10.1007/s12220-020-00543-7zbMath1477.30055arXiv1812.02086OpenAlexW3097533930WikidataQ109744304 ScholiaQ109744304MaRDI QIDQ2050595

Nicola Gigli, Simone Di Marino, Enrico Pasqualetto, Elefterios Soultanis

Publication date: 31 August 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.02086

zbMATH Keywords

Sobolev spacesmetric measure spacesCAT spaces

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) Analysis on metric spaces (30L99)

Related Items (10)

On the structure of RCD spaces with upper curvature bounds ⋮ A differential perspective on gradient flows on \(\mathbf{\mathsf{CAT}} (\kappa)\)-spaces and applications ⋮ Density of subalgebras of Lipschitz functions in metric Sobolev spaces and applications to Wasserstein Sobolev spaces ⋮ Dirichlet problem for harmonic maps from strongly rectifiable spaces into regular balls in \({\mathrm{CAT}}(1)\) spaces ⋮ A short proof of the existence of master test plans ⋮ A note on BV and 1-Sobolev functions on the weighted Euclidean space ⋮ Viscosity solutions of Hamilton-Jacobi equations in proper \(\text{CAT(0)}\) spaces ⋮ Universal infinitesimal Hilbertianity of sub-Riemannian manifolds ⋮ Rectifiability of the reduced boundary for sets of finite perimeter over \(\operatorname{RCD} ( K , N )\) spaces ⋮ Korevaar-Schoen's energy on strongly rectifiable spaces

Cites Work

• Unnamed Item
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• Metric currents and Alberti representations
• Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
• An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature
• Local currents in metric spaces
• Nonlinear potential theory on metric spaces
• Decomposition of acyclic normal currents in a metric space
• Reparametrizations of continuous paths
• Construction of the parallel transport in the Wasserstein space
• Differentiability of Lipschitz functions on metric measure spaces
• Lectures on analysis on metric spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Lipschitz algebras and derivations. II: Exterior differentiation
• Structure of metric cycles and normal one-dimensional currents
• Korevaar-Schoen's directional energy and Ambrosio's regular Lagrangian flows
• CD meets CAT
• Differential of metric valued Sobolev maps
• Ricci curvature for metric-measure spaces via optimal transport
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Plateau's problem for integral currents in locally non-compact metric spaces
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Convex analysis and optimization in Hadamard spaces
• On the differential structure of metric measure spaces and applications
• Differentiation in metric spaces
• Nonsmooth calculus
• Semiconcave functions in Alexandrov's geometry
• An Invitation to Alexandrov Geometry
• Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below
• Sobolev Spaces on Metric Measure Spaces
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
• Currents in metric spaces

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