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Einstein metrics, their moduli spaces and stability
[Submitted on 24 Jul 2025 (v1), last revised 15 Jun 2026 (this v · 2026-06-17 · via math updates on arXiv.org

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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.

Submission history

From: Paul Schwahn [view email]
[v1] Thu, 24 Jul 2025 14:39:13 UTC (50 KB)
[v2] Thu, 16 Oct 2025 22:27:56 UTC (50 KB)
[v3] Mon, 15 Jun 2026 21:15:41 UTC (52 KB)