Quasi-continuous vector fields on RCD spaces

DOI10.1007/s11118-019-09823-6zbMath1457.53032arXiv1903.04302OpenAlexW3007040183WikidataQ109744273 ScholiaQ109744273MaRDI QIDQ2223710

Nicola Gigli, Enrico Pasqualetto, Clément Debin

Publication date: 1 February 2021

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.04302

zbMATH Keywords

quasi-continuitydifferential calculusRCD 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)

Related Items (12)

Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel ⋮ Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds ⋮ Local vector measures ⋮ Constancy of the dimension in codimension one and locality of the unit normal on $\RCD(K,N)$ spaces ⋮ First-order heat content asymptotics on \(\mathsf{RCD} (K, N)\) spaces ⋮ Calculus and fine properties of functions of bounded variation on RCD spaces ⋮ Monotonicity formulas for harmonic functions in \(\mathrm{RCD}(0,N)\) spaces ⋮ Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds ⋮ Subgraphs of BV functions on RCD spaces ⋮ Extremal of log-Sobolev functionals and Li-Yau estimate on \(\mathrm{RCD}^* (K,N)\) spaces ⋮ About the general chain rule for functions of bounded variation ⋮ Rectifiability of the reduced boundary for sets of finite perimeter over \(\operatorname{RCD} ( K , N )\) spaces

Cites Work

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• Non-collapsed spaces with Ricci curvature bounded from below
• 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
• Sobolev Spaces on Metric Measure Spaces
• Volume Estimates on the Critical Sets of Solutions to Elliptic PDEs

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