Related papers: Computations of the orbifold Yamabe invariant

Let $ (M, g) $ be a compact manifold or a complete non-compact manifold without boundary, $ \dim M \geqslant 4 $, and not locally conformally flat. In this article, we introduce a new local method to resolve the Yamabe problem on compact…

Let $(M,g)$ be a compact Riemannian manifold of dimension $n \geq 3$. We define the second Yamabe invariant as the infimum of the second eigenvalue of the Yamabe operator over the metrics conformal to $g$ and of volume 1. We study when it…

The Yamabe invariant Y(M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalar-curvature Riemannian metrics g on M. (To be precise, one only considers those constant-scalar-curvature…

The Yamabe invariant Y(M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalar curvature Riemannian metrics g on M. (To be absolutely precise, one only considers…

We introduce new invariants of a Riemannian singular space, the local Yamabe and Sobolev constants, and then go on to prove a general version of the Yamabe theorem under that the global Yamabe invariant of the space is strictly less than…

Given a conformally variational scalar Riemannian invariant $I$, we identify a sufficient condition for a compact Riemannian manifold to admit finite regular coverings with many nonhomothetic conformal rescalings with $I$ constant. We also…

On a Riemannian compact manifold, we give existence and multiplicity results for solutions of elliptic PDE by introducing isometry invariances. When the groups we used have finite orbits, we get multiplicity results for equations with the…

We establish the existence of an optimal partition for the Yamabe equation in the whole space made up of mutually linearly isometric sets, each of them invariant under the action of a group of linear isometries. To do this, we establish the…

We obtain existence results for a class of fully nonlinear Yamabe-type problems on non-compact manifolds, addressing both the so-called positive and negative cases. We also give explicit examples of manifolds with warped product ends and…

In this work, we study the convergence of the normalized Yamabe flow with positive Yamabe constant on a class of pseudo-manifolds that includes stratified spaces with iterated cone-edge metrics. We establish convergence under a low energy…

We consider several differential-topological invariants of compact 4-manifolds which directly arise from Riemannian variational problems. Using recent results of Bauer and Furuta, we compute these invariants in many cases that were…

We prove several facts about the Yamabe constant of Riemannian metrics on general noncompact manifolds and about S. Kim's closely related "Yamabe constant at infinity". In particular we show that the Yamabe constant depends continuously on…

For a compact connected manifold M of dimension n greater than 3 and with no metric of positive scalar curvature, we prove that the Yamabe invariant is unchanged under surgery on spheres of dimension different from 1, n-2 and n-1. We use…

We consider the equivariant Yamabe problem, i.e. the Yamabe problem on the space of G-invariant metrics for a compact Lie group G. The G-Yamabe invariant is analogously defined as the supremum of the constant scalar curvatures of unit…

We prove a positive mass theorem for some noncompact spin manifolds that are asymptotic to products of hyperbolic space with a compact manifold. As conclusion we show the Yamabe inequality for some noncompact manifolds which are important…

We study the Yamabe problem on open manifolds of bounded geometry and show that under suitable assumptions there exist Yamabe metrics, i.e. conformal metrics of constant scalar curvature. For that, we use weighted Sobolev embeddings.

In this paper, we study scalar curvature rigidity of non-smooth metrics on smooth manifolds with non-positive Yamabe invariant. We prove that if the scalar curvature is not less than the Yamabe invariant in distributional sense, then the…

For an asymptotically Poincare-Einstein manifold with a lower Ricci curvature bound, we establish a sharp inequality relating the type II Yamabe invariant of the interior and the Yamabe invariant of its conformal infinity

This paper concerns a fully nonlinear version of the Yamabe problem on manifolds with boundary. We establish some existence results and estimates of solutions.

The purpose of this article is to study gradient Yamabe soliton on warped product manifolds. First, we prove triviality results in the case of noncompact base with limited warping function, and for compact base. In order to provide…