arXiv subjects

Eric Bahuaud

Publications and source records attributed to Eric Bahuaud.

24 records · Page 2Linked to original sources

arXiv2013

Mapping properties of the heat operator on edge manifolds

We consider the heat operator acting on differential forms on spaces with complete and incomplete edge metrics. In the latter case we study the heat operator of the Hodge Laplacian with algebraic boundary conditions at the edge singularity. We establish the mapping properties of the heat operator, recovering and extending the classical results from smooth manifolds and conical spaces. The estimates, together with strong continuity of the heat operator, yield short-time existence of solutions to certain semilinear parabolic equations. Our discussion reviews and generalizes earlier work by Jeffres and Loya.

math.AP↗

arXiv2011

Ricci flow of conformally compact metrics

In this paper we prove that given a smoothly conformally compact metric there is a short-time solution to the Ricci flow that remains smoothly conformally compact. We adapt recent results of Schnürer, Schulze and Simon to prove a stability result for conformally compact Einstein metrics sufficiently close to the hyperbolic metric.

math.AP↗

arXiv2010

Short-time existence for some higher-order geometric flows

We establish short-time existence and regularity for higher-order flows generated by a class of polynomial natural tensors that, after an adjustment by the Lie derivative of the metric with respect to a suitable vector field, have strongly parabolic linearizations. We apply this theorem to flows by powers of the Laplacian of the Ricci tensor, and to flows generated by the ambient obstruction tensor. As a special case, we prove short-time existence for a type of Bach flow.

math.DG↗

arXiv2008

Conformal compactification of asymptotically locally hyperbolic metrics

In this paper we study the extent to which conformally compact asymptotically hyperbolic metrics may be characterized intrinsically. Building on the work of the first author, we prove that decay of sectional curvature to -1 and decay of covariant derivatives of curvature outside an appropriate compact set yield Hölder regularity for a conformal compactification of the metric. In the Einstein case, we prove that the estimate on the sectional curvature implies the control of all covariant derivatives of the Weyl tensor, permitting us to strengthen our result.

math.DG↗

arXiv2008

Intrinsic characterization for Lipschitz asymptotically hyperbolic metrics

Conformally compact asymptotically hyperbolic metrics have been intensively studied. The goal of this note is to understand what intrinsic conditions on a complete Riemannian manifold (M,g) will ensure that g is asymptotically hyperbolic in this sense. We use the geodesic compactification by asymptotic geodesic rays to compactify M and appropriate curvature decay conditions to study the regularity of the conformal compactification. We also present an interesting example that shows our conclusion is nearly optimal for our assumptions.

math.DG↗

arXiv2006

Hölder Compactification for some manifolds with pinched negative curvature near infinity

We consider a complete noncompact Riemannian manifold M and give conditions on a compact submanifold K of M so that the outward normal exponential map off of the boundary of K is a diffeomorphism onto M\K. We use this to compactify M and show that pinched negative sectional curvature outside K implies M has a compactification with a well defined Hölder structure independent of K. The Hölder constant depends on the ratio of the curvature pinching. This extends and generalizes a 1985 result of Anderson and Schoen.

math.DG↗