Quantitative Stability for Minimizing Yamabe Metrics

2020/09/30 by Max Engelstein, Engelstein, Max, Robin Neumayer +3 · 3 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2009.14362

Abstract

On any closed Riemannian manifold of dimension n≥ 3, we prove that if a function nearly minimizes the Yamabe energy, then the corresponding conformal metric is close, in a quantitative sense, to a minimizing Yamabe metric in the conformal class. Generically, this distance is controlled quadratically by the Yamabe energy deficit. Finally, we produce an example for which this quadratic estimate is false.

Cited by

• The GJMS operators in geometry, analysis, and physics
• Sharp quantitative integral inequalities for harmonic extensions
• Stability of spinorial Sobolev inequalities on \mathbbSⁿ

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