On the long neck principle and width estimates for initial data sets

DOI10.1007/S00209-024-03532-6MaRDI QIDQ6564153

Daoqiang Liu

Publication date: 28 June 2024

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

zbMATH Keywords

initial data setCallias operatorwidth estimatelong neck principle

Mathematics Subject Classification ID

Spin and Spin({}^c) geometry (53C27) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Cites Work

• Metric inequalities with scalar curvature
• Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
• Scalar curvature estimates for compact symmetric spaces.
• Band width estimates via the Dirac operator
• A long neck principle for Riemannian spin manifolds with positive scalar curvature
• Width, largeness and index theory
• Width estimate and doubly warped product
• Four Lectures on Scalar Curvature
• Scalar and mean curvature comparison via \(\mu\)-bubbles
• Scalar Curvature and Generalized Callias Operators
• Quantitative K-Theory, Positive Scalar Curvature, and Bandwidth
• Scalar and mean curvature comparison via the Dirac operator
• A Note on the Long Neck Principle and Spectral Width Inequality of Geodesic Collar Neighborhood
• Spectral torical band inequalities and generalizations of the Schoen-Yau black hole existence theorem
• Positive mass theorems for spin initial data sets with arbitrary ends and dominant energy shields

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