Inversion d'opérateurs de courbures au voisinage de la métrique euclidienne

DOI10.24033/bsmf.2742zbMath1386.53039OpenAlexW2415519302MaRDI QIDQ4635076

Erwann Delay

Publication date: 13 April 2018

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.24033/bsmf.2742

zbMATH Keywords

weighted Sobolev spacesRicci curvaturequasi-linear elliptic PDEsymmetric 2-tensors

Mathematics Subject Classification ID

Differential geometric aspects in vector and tensor analysis (53A45) Elliptic equations on manifolds, general theory (58J05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Perturbations of PDEs on manifolds; asymptotics (58J37) Quasilinear elliptic equations (35J62)

Cites Work

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• Studies of some curvature operators in a neighborhood of an asymptotically hyperbolic Einstein manifold
• Uniqueness and non-existence of metrics with prescribed Ricci curvature
• Obstruction to prescribed positive Ricci curvature
• Existence of metrics with prescribed Ricci curvature: Local theory
• Spectral invariance, ellipticity, and the Fredholm property for pseudodifferential operators on weighted Sobolev spaces
• Metrics with prescribed Ricci curvature of constant rank. I: The integrable case
• Local study of curvature operators on the hyperbolic space
• Ricci curvature in the neighborhood of rank-one symmetric spaces.
• Local solvability of elliptic, and curvature, equations on compact manifolds

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