Elliptic PDEs on Compact Ricci Limit Spaces and Applications

DOI10.1090/memo/1211zbMath1400.53031arXiv1410.3296OpenAlexW4229855509MaRDI QIDQ5376457

Shouhei Honda

Publication date: 18 September 2018

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.3296

zbMATH Keywords

Schrödinger operatorsRicci curvatureGromov-Hausdorff limitelliptic PDEsHodge LaplacianGromov-Hausdorff convergenceYamabe constantsPoisson's equations

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (9)

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 ⋮ Regularity and stability of invariant measures for diffusion processes under synthetic lower Ricci curvature bounds ⋮ Ricci curvature and orientability ⋮ A note on the topological stability theorem from RCD spaces to Riemannian manifolds ⋮ Lichnerowicz-Obata estimate, almost parallel \(p\)-form and almost product manifolds ⋮ Gradient estimates for heat kernels and harmonic functions ⋮ The \(L^p\)-Calderón-Zygmund inequality on non-compact manifolds of positive curvature ⋮ Sphere theorems and eigenvalue pinching without positive Ricci curvature assumption

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