相关论文: Prescribing Morse scalar curvatures: subcritical b…

The problem of prescribing conformally the scalar curvature of a closed Riemannian manifold as a given Morse function reduces to solving an elliptic partial differential equation with critical Sobolev exponent. Two ways of attacking this…

We consider the problem of prescribing conformally the scalar curvature on compact manifolds of positive Yamabe class in dimension $n \geq 5$. We prove new existence results using Morse theory and some analysis on blowing-up solutions,…

We study finite-energy blow-ups for prescribed Morse scalar curvatures in both the subcritical and the critical regime. After general considerations on Palais-Smale sequences we determine precise blow up rates for subcritical solutions: in…

Given a closed manifold of positive Yamabe invariant and for instance positive Morse functions upon it, the conformally prescribed scalar curvature problem raises the question, whether or not such functions can by conformally changing the…

We consider the problem of prescribing the scalar and boundary mean curvatures via conformal deformation of the metric on a $n-$ dimensional compact Riemannian manifold. We deal with the case of negative scalar curvature $K$ and boundary…

Let $(M,g)$ be a complete three dimensional Riemannian manifold with boundary $\partial M$. Given smooth functions $K(x)>0$ and $c(x)$ defined on $M$ and $\partial M$, respectively, it is natural to ask whether there exist metrics conformal…

We consider the classical geometric problem of prescribing the scalar and boundary mean curvatures via conformal deformation of the metric on a $n-$dimensional compact Riemannian manifold. We deal with the case of negative scalar curvature…

In this paper, we investigate the prescribed scalar curvature problem on a non-compact Riemannian manifold $(M, \langle \, , \, \rangle)$, namely the existence of a conformal deformation of the metric $\langle \, , \, \rangle$ realizing a…

We give sufficient and "almost" necessary conditions for the prescribed scalar curvature problems within the conformal class of a Riemannian metric $ g $ for both closed manifolds and compact manifolds with boundary, including the…

A version of the singular Yamabe problem in smooth domains in a closed manifold yields complete conformal metrics with negative constant scalar curvatures. In this paper, we study the blow-up phenomena of Ricci curvatures of these metrics…

We consider the problem of prescribing the Gaussian and the geodesic curvatures of a compact surface with boundary by a conformal deformation of the metric. We derive some existence results using a variational approach, either by…

Let $(M,g)$ be a $n-$dimensional compact Riemannian manifold with boundary. We consider the Yamabe type problem \begin{equation} \left\{ \begin{array}{ll} -\Delta_{g}u+au=0 & \text{ on }M \\ \partial_\nu u+\frac{n-2}{2}bu= u^{{n\over…

In this paper we perform a fine blow-up analysis for a fourth order elliptic equation involving critical Sobolev exponent, related to the prescription of some conformal invariant on the standard sphere. We derive from this analysis some a…

Given a strictly pseudoconvex CR manifold $M$ of dimension three and positive CR Yamabe class, and a positive smooth function $K:M\to\mathbf{R}$ verifying some mild and generic hypotheses, we prove the compactness of the set of solutions of…

We consider a kind of Yamabe problem whose scalar curvature vanishes in the unit ball $\mathbb{B}^n$ and on the boundary $\mathbb{S}^{n-1}$ the mean curvature is prescribed. By combining critical points at infinity approach with Morse…

We illustrate an example of a generic, positive function K on a Riemannian manifold to be conformally prescribed as the scalar curvature, for which the corresponding Yamabe type L2-gradient flow exhibits non compact flow lines, while a…

For the prescribed scalar curvature equation on $S^n$ ($n \ge 6$), we consider the situation where the number of bubbles tends to infinity in the Lyapunov-Schmidt (finite dimension) reduction method. In an outstanding paper by Wei and Yan,…

We consider a linear perturbation of the classical geometric problem of prescribing the scalar and the boundary mean curvature problem in a Riemannian manifold with umbilic boundary provided the Weyl tensor is non-zero everywhere. We will…

Using the Lyapunov-Schmidt reduction method, we describe how to use annular domains to construct (scalar curvature) functions on S^n, (n > 5), so that each one of them enables the conformal scalar curvature equation to have a blowing-up…

The problem of prescribing conformally the scalar curvature on a closed Riemannian manifold of negative Yamabe invariant is always solvable, when the function $K$ to be prescribed is strictly negative, while sufficient and necessary…