Related papers: Rigidity of Poincar\'e-Einstein manifolds with fla…

In this paper, we generalize Huber's finite point conformal compactification theorem to a higher dimensional manifold, which is conformally compact with $L^\frac{n}{2}$ integrable Ricci curvatures.

We study orientability in spaces with Ricci curvature bounded below. Building on the theory developed by Honda, we establish equivalent characterizations of orientability for Ricci limit and RCD spaces in terms of the orientability of their…

We consider complete K\"ahler manifolds with nonnegative Ricci curvature. The main results are: 1. When the manifold has nonnegative bisectional curvature, we show that $\lim\limits_{r\to\infty}\frac{r^{2}}{vol(B(p, r))}\int_{B(p, r)}S$…

Let (M, g) be a compact Einstein manifold with non-empty boundary. We prove that Killing fields at the boundary extend to Killing fields of any (M, g) provided the boundary is weakly convex and a simple condition on the fundamental group…

Let M be a compact manifold with boundary. In this paper, we discuss some rigidity theorems of metrics in a same conformal class that fixes the boundary and satisfy certain integral conditions on the the scalar curvatures and the mean…

This paper is devoted to the study of rigidity properties for special solutions of nonlinear elliptic partial differential equations on smooth, boundaryless Riemannian manifolds. As far as stable solutions are concerned, we derive a new…

The sharp isoperimetric inequality for non-compact Riemannian manifolds with non-negative Ricci curvature and Euclidean volume growth has been obtained in increasing generality with different approaches in a number of contributions…

The goal of this article is to study compact quasi-Einstein manifolds with boundary. We provide boundary estimates for compact quasi-Einstein manifolds simi\-lar to previous results obtained for static and $V$-static spaces. In addition, we…

For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality…

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products…

We consider solutions to some semilinear elliptic equations on complete noncompact Riemannian manifolds and study their classification as well as the effect of their presence on the underlying manifold. When the Ricci curvature is…

The volume entropy of a compact metric measure space is known to be the exponential growth rate of the measure lifted to its universal cover at infinity. For a compact Riemannian $n$-manifold with a negative lower Ricci curvature bound and…

We investigate the geometry and topology of compact submanifolds of arbitrary codimension in space forms satisfying a certain pinching condition involving the length of the second fundamental form and the mean curvature. We prove that this…

This paper is devoted to the Moser-Trudinger-Onofri inequality on smooth compact connected Riemannian manifolds. We establish a rigidity result for the Euler-Lagrange equation and deduce an estimate of the optimal constant in the inequality…

In this paper, we study geometric rigidity of Riemannian manifolds admitting stable solutions of certain elliptic problems (stability in a variational sense), that is, under suitable hypotheses, we are able to characterize the Riemannian…

For three dimensional complete, non-compact Riemannian manifolds with non-negative Ricci curvature and uniformly positive scalar curvature, we obtain the sharp linear volume growth ratio and the corresponding rigidity.

Ejiri gave a negative answer to a conjecture of Lichnerowicz concerning Riemannian manifolds with constant scalar curvature admitting an infinitesimal non isometric conformal transformation. With this aim he constructed a warped product of…

In this paper we show that a $\rho$-Einstein solitons conformal to a pseudo-Euclidean space, invariant under the action of the pseudo-orthogonal group with zero scalar curvature is stady and consequently flat. How application of the results…

In this paper we consider Riemannian manifolds of dimension at least $3$, with nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset with smooth boundary we establish the validity of an optimal Minkowski…

We provide a somewhat geometric proof of a rigidity theorem by M. Ledoux and C. Xia concerning complete manifolds with non-negative Ricci curvature supporting an Euclidean-type Sobolev inequality with (almost) best Sobolev constant. Using…