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arXiv · 2508.06633

Linear and nonlinear stability for the Bach flow, I

Eric Bahuaud·Christine Guenther·James Isenberg·Rafe Mazzeo
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Abstract

In this paper we prove the linear stability of a gauge-modified version of the Bach flow on any complete manifold (M, h) of constant curvature. This involves some intricate calculations to obtain spectral bounds, and in particular introduces a higher order generalization of the well-known Koiso identity. We also prove nonlinear stability for the Bach flow if (M, h) is hyperbolic space, and more generally any Poincar\'e-Einstein space sufficiently close to h. In the forthcoming Part II of this project, we study the nonlinear stability question if M is either compact or else noncompact and flat, since those cases require different considerations involving a center manifold.

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Eric Bahuaud, Christine Guenther, James Isenberg, Rafe Mazzeo. 2025-08-08. Linear and nonlinear stability for the Bach flow, I. https://arxiv.org/abs/2508.06633

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