Related papers: Yamabe metrics on conical manifolds

We let (M^m, g) be a closed smooth Riemannian manifold (m >1) with positive scalar curvature S_g, and prove that the Yamabe constant of (M \times R^n,g+g_E) is achieved by a metric in the conformal class of (g+g_E), where g_E is the…

Given a smooth compact manifold with boundary, we study variational properties of the volume functional and of the area functional of the boundary, restricted to the space of the Riemannian metrics with prescribed curvature. We obtain a…

In this note we prove an existence result for the Einstein conformal constraint equations for metrics with vanishing Yamabe invariant assuming that the TT-tensor is small in $L^2$.

We show that the Calabi-Yau metrics with isolated conical singularities of Hein-Sun admit polyhomogeneous expansions near their singularities. Moreover, we show that, under certain generic assumptions, natural families of smooth Calabi-Yau…

In this paper we investigate the structure of certain solutions of the fully nonlinear Yamabe flow, which we call quotient almost Yamabe solitons because they extend quite naturally those called quotient Yamabe solitons. We then present…

We consider the problem of constructing solutions to the Yamabe equation (i.e. conformal constant scalar curvature metrics) on the generalized connected sum M = (M_1) #_K (M_2) of two compact Riemannian manifolds (M_1,g_1) and (M_2,g_2)…

We show a surgery formula for the relative Yamabe invariant and give applications to the study of concordance classes of metrics.

We discuss the constant $\sigma_{2}$ problem for conic 4-spheres. Based on earlier works of Chang-Han-Yang and Han-Li-Teixeira, we are able to find a necessary condition for the existence problem. In particular, when the condition is sharp,…

We prove that the problem of constructing biharmonic conformal maps on a $4$-dimensional Einstein manifold reduces to a Yamabe-type equation. This allows us to construct an infinite family of examples on the Euclidean 4-sphere. In addition,…

We prove the existence of Sasakian-Einstein metrics on infinitely many rational homology spheres in all odd dimensions greater than 3. In dimension 5 we obain somewhat sharper results. There are examples where the number of effective…

We continue our study, initiated in our earlier paper, of Riemann surfaces with constant curvature and isolated conic singularities. Using the machinery developed in that earlier paper of extended configuration families of simple divisors,…

An orbifold version of the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics. Also, several estimates for the orbifold Yamabe invariants of weighted projective spaces…

We prove that the Yamabe invariant of any simply connected smooth manifold of dimension n greater than four is non-negative. Equivalently that the infimum of the L^{n/2} norm of the scalar curvature, over the space of all Riemannian metrics…

We prove nonuniqueness results for constant sixth order $Q$-metrics on complete locally conformally flat $n$-dimensional Riemannian manifolds with $n\geqslant 7$. More precisely, assuming a positive Green function exists for the sixth order…

We develop a general regulated volume expansion for the volume of a manifold with boundary whose measure is suitably singular along a separating hypersurface. The expansion is shown to have a regulator independent anomaly term and a…

For each $n\ge 3$, we construct on $\mathbb{C}^n$ examples of complete Calabi-Yau metrics of Euclidean volume growth having a tangent cone at infinity with singular cross-section.

The Yamabe invariant is a diffeomorphism invariant of smooth compact manifolds that arises from the normalized Einstein-Hilbert functional. This article highlights the manner in which one compelling open problem regarding the Yamabe…

The fractional Yamabe problem, proposed by Gonz\'{a}lez-Qing (2013, Anal. PDE) is a geometric question which concerns the existence of metrics with constant fractional scalar curvature. It extends the phenomena which were discovered in the…

In this paper we derive a refined asymptotic expansion, near an isolated singularity, for conformally flat metrics with constant positive Q-curvature and positive scalar curvature. The condition that the metric has constant Q-curvature…

Let M,g a compact Riemannian n-dimensional manifold. It is well know that, under certain hypothesis, in the conformal class of g there are scalar-flat metrics that have the boundary of M as a constant mean curvature hypersurface. Also,…