Geodesic balls in a simply connected space forms, or are distinguished manifolds for
comparison in bounded Riemannian geometry. In this paper we show that they have the …

The goal of this paper is to study weakly Einstein critical metrics of the volume functional on
a compact manifold M with smooth boundary∂ M. Here, we will give the complete …

We prove that a critical metric of the volume functional on a 4-dimensional compact manifold
with boundary satisfying a second-order vanishing condition on the Weyl tensor must be …

The aim of this paper is to study compact Riemannian manifolds (M,\, g)(M, g) that admit a
non-constant solution to the system of equations-Δ f\, g+ Hess f-fRic= μ Ric+ λ g,-Δ fg+ H essf …

It is shown that the mass of an asymptotically flat manifold with a noncompact boundary can
be computed in terms of limiting surface integrals involving the Einstein tensor of the interior …

We provide an isoperimetric inequality for critical metrics of the volume functional with
nonnegative scalar curvature on compact manifolds with boundary. In addition, we establish …

The aim of this paper is to present a version of the generalized Pohozaev-Schoen identity in
the context of asymptotically euclidean manifolds. Since these kind of geometric identities …

In this article, we investigate the geometry of critical metrics of the volume functional on an n-
dimensional compact manifold with (possibly disconnected) boundary. We establish sharp …

Esse trabalho está dividido em duas partes e tem como objetivo estudar campos conformes
e métricas crıticas em variedades compactas com bordo. A primeira dessas partes está …

Mostra-se que a massa e o centro de massa de uma variedade riemanniana
assintoticamente plana com bordo nao compacto podem ser calculados como o limite …