Einstein metrics, their moduli spaces and stability

2025/07/24 by Paul Schwahn, Uwe Semmelmann, Schwahn, Paul +1 · 1 citation
Mathematics · Physics and Astronomy · #53C21 #53C24 #53C25 #53E20 #58D27 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2507.18463

openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/08/01

Abstract

This survey deals with two closely connected topics: first, the stability of Einstein metrics under the Einstein-Hilbert functional, and second, their deformation theory and the study of the moduli space of Einstein metrics on a compact manifold. To first order, both problems reduce to studying the spectrum and eigentensors of the Lichnerowicz Laplacian. We give an introduction to the classical theory and survey recent results and advances.

Cited by

• Ricci flow and the scalar curvature rigidity of Einstein manifolds

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