Eric Bahuaud
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View article: Linear and nonlinear stability for the Bach flow, I
Linear and nonlinear stability for the Bach flow, I Open
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 introduc…
View article: Extreme 5-dimensional black holes with SU(2)-symmetric horizons
Extreme 5-dimensional black holes with SU(2)-symmetric horizons Open
A bstract We show that the near horizon geometry of 5-dimensional extreme (i.e., degenerate) stationary vacuum black holes, with or without cosmological constant, whose event horizons exhibit SU(2) symmetry must be that of a Berger sphere.
View article: Extreme 5-dimensional black holes with SU(2)-symmetric horizons
Extreme 5-dimensional black holes with SU(2)-symmetric horizons Open
We show that the near horizon geometry of 5-dimensional extreme (i.e., degenerate) stationary vacuum black holes, with or without cosmological constant, whose event horizons exhibit $\SU(2)$ symmetry must be that of a Berger sphere.
View article: Deformations of the Kerr-(A)dS near horizon geometry
Deformations of the Kerr-(A)dS near horizon geometry Open
We investigate deformations of the Kerr-(A)dS near horizon geometry and derive partial infinitesimal rigidity results for it. The proof comprises two parts. First, we follow the analysis of Jezierski and Kamiński (2013 Gen. Rel. Grav. 45 9…
View article: Deformations of the Kerr-(A)dS Near Horizon Geometry
Deformations of the Kerr-(A)dS Near Horizon Geometry Open
We investigate deformations of the Kerr-(A)dS near horizon geometry and derive partial infinitesimal rigidity results for it. The proof comprises two parts. First, we follow the analysis of Jezierski and Kamiński [Gen Rel Grav 45 (2013) 98…
View article: Rigidity of quasi-Einstein metrics: The incompressible case
Rigidity of quasi-Einstein metrics: The incompressible case Open
As part of a programme to classify quasi-Einstein metrics $(M,g,X)$ on closed manifolds and near-horizon geometries of extreme black holes, we study such spaces when the vector field $X$ is divergence-free but not identically zero. This co…
View article: Convergence stability for Ricci flow on manifolds with bounded geometry
Convergence stability for Ricci flow on manifolds with bounded geometry Open
We prove that the Ricci flow for complete metrics with bounded geometry depends continuously on initial conditions for finite time with no loss of regularity. This relies on our recent work where sectoriality for the generator of the Ricci…
View article: Wellposedness of nonlinear flows on manifolds of bounded geometry
Wellposedness of nonlinear flows on manifolds of bounded geometry Open
We present simple conditions which ensure that a strongly elliptic operator $L$ generates an analytic semigroup on Hölder spaces on an arbitrary complete manifold of bounded geometry. This is done by establishing the equivalent property th…
View article: Static near horizon geometries and rigidity of quasi-Einstein manifolds
Static near horizon geometries and rigidity of quasi-Einstein manifolds Open
Static vacuum near horizon geometries are solutions $(M,g,X)$ of a certain quasi-Einstein equation on a closed manifold $M$, where $g$ is a Riemannian metric and $X$ is a closed 1-form. It is known that when the cosmological constant vanis…
View article: Sectoriality of the Laplacian on Asymptotically Hyperbolic Spaces
Sectoriality of the Laplacian on Asymptotically Hyperbolic Spaces Open
We prove that both the Laplacian on functions, and the Lichnerowicz Laplacian on symmetric 2-tensors with respect to asymptotically hyperbolic metrics, are sectorial maps in weighted Hölder spaces. As an application, the machinery of analy…
View article: Apollonian sets in taxicab geometry
Apollonian sets in taxicab geometry Open
Fix two points $p$ and $q$ in the plane and a positive number $k \neq 1$. A result credited to Apollonius of Perga states that the set of points $x$ that satisfy $d(x, p)/d(x, q) = k$ forms a circle. In this paper we study the analogous se…
View article: Ricci Flow and Volume Renormalizability
Ricci Flow and Volume Renormalizability Open
With respect to any special boundary defining function, a conformally compact asymptotically hyperbolic metric has an asymptotic expansion near its conformal infinity. If this expansion is even to a certain order and satisfies one extra co…
View article: Long-time existence of the edge Yamabe flow
Long-time existence of the edge Yamabe flow Open
This article presents an analysis of the normalized Yamabe flow starting at and preserving a class of compact Riemannian manifolds with incomplete edge singularities and negative Yamabe invariant. Our main results include uniqueness, long-…
View article: Asymptotically hyperbolic normalized Ricci flow and rotational symmetry
Asymptotically hyperbolic normalized Ricci flow and rotational symmetry Open
We consider the normalized Ricci flow evolving from an initial metric which is conformally compactifiable and asymptotically hyperbolic. We show that there is a unique evolving metric which remains in this class, and that the flow exists u…
View article: Low regularity Poincaré-Einstein metrics
Low regularity Poincaré-Einstein metrics Open
We prove the existence of a $C^{1,1}$ conformally compact Einstein metric on the ball that has asymptotic sectional curvature decay to $-1$ plus terms of order $e^{-2r}$ where $r$ is the distance from any fixed compact set. This metric has…