Related papers: Conformal Metrics with Constant Q-Curvature
Complete constant positive scalar curvature metrics on S^n - {p_1, ..., p_k} admit a definite asymptotic structure; i.e. the metric is asymptotic to a specific S^{n-1}-invariant metric near the puncture points. This allows one to glue…
In the paper two important theorems about complete affine spheres are generalized to the case of statistical structures on abstract manifolds. The assumption about constant sectional curvature is replaced by the assumption that the…
We investigate compact complex manifolds endowed with SKT or balanced metrics. In each case we define a new functional whose critical points are proved to be precisely the K\"ahler metrics, if any, on the manifold. As general manifolds of…
In this paper it is hown that given any smooth, positive function f on a closed, smooth manifold of dimension greater than four and with positive Paneitz invariant, there exists a metric on M such that $Q_g$ = f.
The Lagrangian of Quantum Chromodynamics is invariant under conformal transformations. Although this symmetry is broken by quantum corrections, it has important consequences for strong interactions at short distances and provides one with…
We study two types of isotropic planes: weakly isotropic and strongly isotropic planes. We prove that a Riemannian manifold of indefinite metric is conformally flat if and only if its curvature tensor vanishes on all the strongly isotropic…
We devise a geometric description of bounded systems at criticality in any dimension $d$. This is achieved by altering the flat metric with a space dependent scale factor $\gamma(x)$, $x$ belonging to a general bounded domain $\Omega$.…
In this paper, we show that the constant property of the Gaussian curvature of surfaces of revolution in both $\mathbb R^4$ and $\mathbb R_1^4$ depend only on the radius of rotation. We then give necessary and sufficient conditions for the…
We provide some obstructions to the prescribed Q-curvature problem for the complete conformal metrics on $\mathbb{R}^n$ with finite total Q-curvature. One of them is a Bonnet-Mayer type theorem with respect to Q-curvature. Others are…
Let (M,g) be a compact Riemannian manifold with dimension n > 2. The Yamabe problem is to find a metric with constant scalar curvature in the conformal class of g, by minimizing the total scalar curvature. The proof was completed in 1984.…
This paper focuses on the problem of prescribing mean curvature on the unit ball. Assume that $f$, which is allowed to change sign, satisfies Morse index counting or certain kind of symmetry condition. By using a negative gradient flow…
We show that a $3-$dimensional paracontact manifold on which $Q\varphi =\varphi Q$ is either a manifold with $trh^2=0$, flat or of constant $\xi-$sectional curvature $k\neq-1$ and constant $\varphi$-sectional curvature $-k\neq 1$.
The change of conformal moduli of polygonal quadrilaterals under some geometric transformations is studied. We consider the motion of one vertex when the other vertices remain fixed, the rotation of sides, polarization, symmetrization, and…
A simple proof is given of the necessary and sufficient condition on a triple of positive numbers A,B,C for the existence of a conformal metric of constant positive curvature on the sphere, with three conic singularities of total angles…
In this paper, we explore the conformal structure of singularities arising from varying fundamental constants using the method of Penrose diagrams. We employ a specific type of bimetric model featuring two different metrics. One metric…
In this paper we revisit the $\sigma_k$-Yamabe problem on $M^n$, namely, finding a conformal metric with constant $\sigma_k$-scalar curvature. We prove that on a closed manifold $\left(M,\left[g_0\right]\right)$ with positive Yamabe…
The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this…
Given a metric defined on a manifold of dimension three, we study the problem of finding a conformal filling by a Poincar\'e-Einstein metric on a manifold of dimension four. We establish a compactness result for classes of conformally…
We prove the rigidity of rectifiable boundaries with constant distributional mean curvature in the Brendle class of warped product manifolds (which includes important models in General Relativity, like the deSitter--Schwarzschild and…
We study conformal metrics on $R^3$, i.e., metrics of the form $g_u=e^{2u}|dx|^2$, which have constant $Q$-curvature and finite volume. This is equivalent to studying the non-local equation $$ (-\Delta)^\frac32 u = 2 e^{3u}$$ in $R^3$…