Related papers: Conformal extremal metrics and constant scalar cur…

A conformal metric $g$ with constant curvature one and finite conical singularities on a compact Riemann surface $\Sigma$ can be thought of as the pullback of the standard metric on the 2-sphere by a multi-valued locally univalent…

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…

Let $(M, \bar g)$ be an $n$-dimensional complete Riemannian manifold. In this paper, we considers the following conformal scalar curvature rigidity problem: Given a compact smooth domain $\Omega$ with $\partial \Omega$, can one find a…

In this paper, we consider the problem of existence and multiplicity of conformal metrics on a riemannian compact $4-$dimensional manifold $(M^4,g_0)$ with positive scalar curvature. We prove new exitence criterium which provides existence…

Let $(M,g)$ be an $n-$dimensional compact Riemannian manifold. Let $h$ be a smooth function on $M$ and assume that it has a critical point $\xi\in M$ such that $h(\xi)=0$ and which satisfies a suitable flatness assumption. We are interested…

In this paper we prove that, given a compact four dimensional smooth Riemannian manifold (M,g) with smooth boundary there exists a metric conformal to g with constant T-curvature, zero Q-curvature and zero mean curvature under generic and…

We study the Euler-Lagrange equation for several natural functionals defined on a conformal class of almost Hermitian metrics, whose expression involves the Lee form $\theta$ of the metric. We show that the Gauduchon metrics are the unique…

In 1977, Gauduchon proved that on every compact hermitian manifold $(X, \omega)$ there exists a conformally equivalent hermitian metric $\omega_{\mathrm{G}}$ which satisfies $\mathrm{dd}^c \omega_{\mathrm{G}}^{n-1} = 0$. In this note, we…

If a smooth compact 4-manifold M admits a Kaehler-Einstein metric g of positive scalar curvature, Gursky showed that its conformal class [g] is an absolute minimizer of the Weyl functional among all conformal classes with positive Yamabe…

The paper is an attempt to resolve the prescribed Chern scalar curvature problem. We look for solutions within the conformal class of a fixed Hermitian metric. We divide the problem in three cases, according to the sign of the Gauduchon…

We consider the problem of finding on a given Euclidean domain $\Omega$ of dimension $n \geq 3$ a complete conformally flat metric whose Schouten curvature $A$ satisfies some equation of the form $f(\lambda(-A)) = 1$. This generalizes a…

Let $(M, g)$ be a compact Riemannian manifold with boundary $\partial M$. Given a function $f$ on $\partial M$, we consider the problem of finding a conformal metric of $g$ with zero scalar curvature in $M$ and prescribed mean curvature $f$…

Given a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure.…

On a smooth, closed Riemannian manifold $(M,g)$ of dimension $n\ge3$ with positive scalar curvature and not conformally diffeomorphic to the standard sphere, we prove that the only conformal metrics to $g$ with constant Q-curvature of order…

Let $R$ be a constant. Let $\mathcal{M}^R_\gamma$ be the space of smooth metrics $g$ on a given compact manifold $\Omega^n$ ($n\ge 3$) with smooth boundary $\Sigma $ such that $g$ has constant scalar curvature $R$ and $g|_{\Sigma}$ is a…

We study the problem of deforming a Riemannian metric to a conformal one with nonzero constant scalar curvature and nonzero constant boundary mean curvature on a compact manifold of dimension $n\geq 3$. We prove the existence of such…

We consider the conformal class of the Riemannian product $g_0 + g$, where $g_0$ is the constant curvature metric on $S^m$ and $g$ is a metric of constant scalar curvature on some closed manifold. We show that the number of metrics of…

Let \((M^n,g)\) be a smooth closed Riemannian manifold of dimension \(n \ge 5\) with positive Yamabe invariant and semi-positive \(Q\)-curvature. We establish a precompactness result in the \(C^{\alpha}\)-H\"older topologie on the space of…

Let $(M^n,g),~n\ge 3$ be a noncompact complete Riemannian manifold with compact boundary and $f$ a smooth function on $\partial M$. In this paper we show that for a large class of such manifolds, there exists a metric within the conformal…

Let $(M,g)$ be a two dimensional compact Riemannian manifold of genus $g(M)>1$. Let $f$ be a smooth function on $M$ such that $$f \ge 0, \quad f\not\equiv 0, \quad \min_M f = 0. $$ Let $p_1,\ldots,p_n$ be any set of points at which…