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Local structure theory of Einstein manifolds with boundary

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arxiv 2405.17577 v1 pith:H46AGFZI submitted 2024-05-27 math.DG gr-qc

Zhongshan An , Lan-Hsuan Huang This is my paper · ORCID
classification math.DGgr-qc
keywords boundaryeinsteinmetricslocalstructurethreeandersoncompact
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We study local structure of the moduli space of compact Einstein metrics with respect to the boundary conformal metric and mean curvature. In dimension three, we confirm M. Anderson's conjecture in a strong sense, showing that the map from Einstein metrics to such boundary data is generically a local diffeomorphism. In dimensions greater than three, we obtain similar results for Ricci flat metrics and negative Einstein metrics under new non-degenerate boundary conditions.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the Stability of Einstein Manifolds with Boundary

    math.DG 2026-07 conditional novelty 6.5 of 10

    Einstein manifolds with boundary are analyzed for Einstein-Hilbert stability via TVg tensors; Schwarzschild-AdS is mode-stable at R=((n-1)m)^{1/(n-3)} under spherical perturbations, while 4D Schwarzschild is unstable ...

  2. Unifying Model-Free Efficiency and Model-Based Representations via Latent Dynamics

    cs.LG 2026-02 reject novelty 4.0 of 10

    ULD claims that a model-free RL algorithm with value-aligned latent representations and no planning can match model-based generalists across 80 environments, but the theoretical support is mostly restatement and the e...

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