9 citations · 13 across the 7 of their papers we have counts for
9 papers
Positive Einstein metrics on infinitely many four-manifolds
Tristan Ozuch
We construct smooth Einstein metrics with positive scalar curvature on and on , for $k…
Stability of gravitational instantons with a bounded Killing vector field
Tristan Ozuch
We prove that a complete ALF Ricci-flat 4-manifold carrying a bounded Killing vector field is linearly stable if and only if it is locally hyperkähler. This applies uniformly to al…
Desingularizations of Conformally Kaehler, Einstein Orbifolds
Claude LeBrun, Tristan Ozuch
Let {(M,g_i)} be a sequence of smooth compact oriented Einstein 4-manifolds of fixed Einstein constant that Gromov-Hausdorff converges to a 4-dimensional Einstein orbifold X…
Regularity of Einstein 5-manifolds via 4-dimensional gap theorems
Yiqi Huang, Tristan Ozuch
We refine the regularity of noncollapsed limits of 5-dimensional manifolds with bounded Ricci curvature. In particular, for noncollapsed limits of Einstein 5-manifolds, we prove th…
Instability of conformally Kähler, Einstein metrics
Olivier Biquard, Tristan Ozuch
We prove the instability of conformally Kähler, compact or ALF Einstein 4-manifolds with nonnegative scalar curvature which are not half conformally flat. This applies to all the k…
Integrability of Einstein deformations and desingularizations
Tristan Ozuch
We study the question of the integrability of Einstein deformations and relate it to the question of the desingularization of Einstein metrics. Our main application is a negative a…
Higher order obstructions to the desingularization of Einstein metrics
Tristan Ozuch
We find new obstructions to the desingularization of compact Einstein orbifolds by smooth Einstein metrics. These new obstructions, specific to the compact situation, raise the que…
Noncollapsed degeneration of Einstein 4-manifolds II
Tristan Ozuch
In this second article, we prove that any desingularization in the Gromov-Hausdorff sense of an Einstein orbifold is the result of a gluing-perturbation procedure that we develop.…
Noncollapsed degeneration of Einstein 4-manifolds I
Tristan Ozuch
A theorem of Anderson and Bando-Kasue-Nakajima from 1989 states that to compactify the set of normalized Einstein metrics with a lower bound on the volume and an upper bound on the…