Critical metrics of the volume functional with pinched curvature

DOI10.1215/00192082-10972626arXiv2202.08652MaRDI QIDQ6183833

C. Queiroz, Halyson I. Baltazar

Publication date: 4 January 2024

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.08652

zbMATH Keywords

volume functionalWeyl curvatureMiao-Tam critical metrics

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global Riemannian geometry, including pinching (53C20) Rigidity results (53C24) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Cites Work

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• Critical metrics of the volume functional on compact three-manifolds with smooth boundary
• Volume functional of compact 4-manifolds with a prescribed boundary metric
• On critical point equation of compact manifolds with zero radial Weyl curvature
• On static manifolds and related critical spaces with zero radial Weyl curvature
• Einstein and conformally flat critical metrics of the volume functional
• On the volume functional of compact manifolds with harmonic Weyl tensor

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