Related papers: Survey: Homogeneous Einstein Manifolds

Smooth Kahler-Einstein metrics have been studied for the past 80 years. More recently, singular Kahler-Einstein metrics have emerged as objects of intrinsic interest, both in differential and algebraic geometry, as well as a powerful tool…

We consider hypersurfaces in Einstein-Sasaki 5-manifolds which are tangent to the characteristic vector field. We introduce evolution equations that can be used to reconstruct the 5-dimensional metric from such a hypersurface, analogous to…

Two recently published papers (J.D. Barrow and A. Paliathanasis, Eur. Phys. J. C. (2018, 2019)) claim to have found exact solutions of Einstein's field equations belonging to the class of non-trivial Szekeres models, whose source is a…

We study homogeneous curves on some classes of reductive homogeneous spaces G=H which are geodesics with respect to any G-invariant metric on G=H. These curves are called equigeodesics. The spaces we consider are certain Stiefel manifolds…

The aim of this note is the study of Einstein condition for para-holomorphic Riemannian metrics in the para-complex geometry framework. Firstly, we make some general considerations about para-complex Riemannian manifolds (not necessarily…

We give an elementary treatment of the existence of complete Kahler-Einstein metrics with nonpositive Einstein constant and underlying manifold diffeomorphic to the tangent bundle of the (n+1)-sphere.

In this note, we give a brief survey on some recent developments of biharmonic submanifolds. After reviewing some recent progress on Chen's biharmonic conjecture, the Generalized Chen's conjecture on biharmonic submanifolds of…

The evolution of the methods used to find solutions of Einstein's field equations during the last 100 years is described. Early papers used assumptions on the coordinate forms of the metrics. Since the 1950s more invariant methods have been…

In this article we are interested in quantitative homogenization results for linear elliptic equations in the non-stationary situation of a straight interface between two heterogenous media. This extends the previous work [Josien, 2019] to…

We study the space of oriented genus g subsurfaces of a fixed manifold M, and in particular its homological properties. We construct a "scanning map" which compares this space to the space of sections of a certain fibre bundle over M…

We study infinitesimal Einstein deformations on compact flat manifolds and on product manifolds. Moreover, we prove refinements of results by Koiso and Bourguignon which yield obstructions on the existence of infinitesimal Einstein…

We demonstrate the homogeneity of the Hilbert Cube. In particular, we construct explicit self-homeomorphisms of the Hilbert cube so that given any two points, a homeomorphism moving one to the other may be realized.

In this article, we consider Einstein-type manifolds with boundary which generalizes important geometric equations, like static vacuum and static perfect fluid. We investigate some geometric inequalities for those manifolds. Then, we…

We revisit the homogeneous and inhomogeneous Dirichlet problem for the Laplacian on Lipschitz domains. This is motivated by the recent postings by Amrouche and Moussaoui which purport to contradict known area integral estimates of Dahlberg…

This survey on flexible Weinstein manifolds is, essentially, an extract from our recent joint book.

This paper investigates quantitative estimates in the homogenization of second-order elliptic systems with periodic coefficients that oscillate on multiple separated scales. We establish large-scale interior and boundary Lipschitz estimates…

In this paper we generalize Wiener's characterization of continuous measures to compact homogenous manifolds. In particular, we give necessary and sufficient conditions on probability measures on compact semisimple Lie groups and…

Let (M,g) be a compact Einstein manifold with smooth boundary. We consider the spectrum of the p form valued Laplacian with respect to a suitable boundary condition. We show that certain geometric properties of the boundary may be…

Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…

A response to a letter to the editor by Schilling regarding Bartroff, Lorden, and Wang ("Optimal and fast confidence intervals for hypergeometric successes" 2022, arXiv:2109.05624)