Related papers: Regularity of Einstein 5-manifolds via 4-dimension…

Let $(M,g_0)$ be a compact $n$-dimensional Riemannian manifold with a finite number of singular points, where the metric is asymptotic to a non-negatively curved cone over $(\mathbb{S}^{n-1},g)$. We show that there exists a smooth Ricci…

In this paper, first we consider the existence and non-existence of Einstein metrics on the topological 4-manifolds $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$ (for $k \in {11, 13, 14, 15, 16, 17, 18}$) by using the idea of R\u{a}sdeaconu and…

Biconformal deformations take place in the presence of a conformal foliation, deforming by different factors tangent to and orthogonal to the foliation. Four-manifolds endowed with a conformal foliation by surfaces present a natural context…

This paper is devoted to the first systematic investigation of manifolds that are Einstein for a connection with skew symmetric torsion. We derive the Einstein equation from a variational principle and prove that, for parallel torsion, any…

We establish codimension 4 regularity of noncollapsed sequences of metrics with bounds on natural generalizations of the Ricci tensor. We obtain a priori L2 curvature estimates on such spaces, with diffeomorphism finiteness results and…

Consider a Riemannian manifold with bounded Ricci curvature $|\Ric|\leq n-1$ and the noncollapsing lower volume bound $\Vol(B_1(p))>\rv>0$. The first main result of this paper is to prove that we have the $L^2$ curvature bound…

We set up an Einstein-Gauss-Bonnet theory in four dimensions, based on the recent formulation of pure gravity with extra dimensions of vanishing metrical length [1]. In absence of torsion, the effective field equations depend only on the…

We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of…

We prove that complete warped product Einstein metrics with isometric bases, simply connected space form fibers, and the same Ricci curvature and dimension are isometric. In the compact case we also prove that the warping functions must be…

Building on previous results, we complete the classification of compact oriented Einstein 4-manifolds with det (W^+) > 0. There are, up to diffeomorphism, exactly 15 manifolds that carry such metrics, and, on each of these manifolds, such…

Gompf's end-sum techniques are used to establish the existence of an infinity of non-diffeomorphic manifolds, all having the same trivial ${\bf R^4}$ topology, but for which the exotic differentiable structure is confined to a region which…

We prove that there are infinitely many pairs of homeomorphic non-diffeomorphic smooth 4-manifolds, such that in each pair one manifold admits an Einstein metric and the other does not. We also show that there are closed 4-manifolds with…

We give new examples of compact, negatively curved Einstein manifolds of dimension $4$. These are seemingly the first such examples which are not locally homogeneous. Our metrics are carried by a sequence of 4-manifolds $(X_k)$ previously…

In this paper, we derive the uniform L^{4}-bound of the transverse conic Ricci curvature along the conic Sasaki-Ricci flow on a compact transverse log Fano Sasakian manifold M of dimension five and the space of leaves of the characteristic…

In a recent article the first three authors proved that in dimension $4m+1$ all homotopy spheres that bound parallelizable manifolds admit Einstein metrics of positive scalar curvature which, in fact, are Sasakian-Einstein. They also…

In this paper, we obtain classification of four-dimensional Einstein manifolds with positive Ricci curvature and pinched sectional curvature. In particular, the first result concerns with an upper bound of sectional curvature, improving a…

We show that K\"ahler-Einstein metrics with cone singularities along simple normal crossing (SNC) divisors define RCD spaces, both in the compact setting and in certain non-compact cases, thereby producing many examples of Einstein RCD…

We prove the existence of Sasaki-Einstein metrics on certain simply connected 5-manifolds where until now existence was unknown. All of these manifolds have non-trivial torsion classes. On several of these we show that there are a countable…

We prove that for a residual (and hence dense) subset $\mathcal{G}$ of Riemannian metrics on $S^{n+1}$ in the $C^{3}$ topology, no area-minimizing integral $n$-current that is a boundary admits a singular tangent cone which is linearly…

We study the structure of Gromov-Hausdorff limits of sequences of Riemannian manifolds $\{(M_\alpha^n,g_\alpha)\}_{\alpha \in A}$ whose Ricci curvature satisfies a uniform Kato bound. We first obtain Mosco convergence of the Dirichlet…