Related papers: Computations of the orbifold Yamabe invariant

In the context of Berglund-Huebsch mirror symmetry, we compute the eigenvalues of the Frobenius endomorphism acting on a p-adic version of Borisov's complex. As a result, we conjecture an explicit formula for the number of points of crepant…

We give a characterization of conformal classes realizing a compact manifold's Yamabe invariant. This characterization is the analogue of an observation of Nadirashvili for metrics realizing the maximal first eigenvalue, and of Fraser and…

In this paper, we study multiplicity of solutions of the Yamabe problem on product manifolds with minimal boundary via bifurcation theory.

By using the fiberwise spherical symmetrization we give a comparison theorem of Yamabe constants on warped products and prove the existence of radially-symmetric Yamabe minimizers on Riemannian manifolds given by products with round…

By using variational techniques we provide new existence results for Yamabe-type equations with subcritical perturbations set on a compact $d$-dimensional ($d\geq 3$) Riemannian manifold without boundary. As a direct consequence of our main…

We consider a nonlinear version of the Yamabe problem on locally conformally flat compact manifolds with boundary. The main technique we used is to derive boundary $C^2$ estimates directly from boundary $C^0$ estimates. In particular, the…

We study in this paper the fractional Yamabe problem first considered by Gonzalez-Qing on the conformal infinity $(M^n , [h])$ of a Poincar\'e-Einstein manifold $(X^{n+1} , g^+ )$ with either $n = 2$ or $n \geq 3$ and $(M^n , [h])$ is…

In conformal geometry, the Compactness Conjecture asserts that the set of Yamabe metrics on a smooth, compact, aspherical Riemannian manifold (M,g) is compact. Established in the locally conformally flat case by Schoen [43,44] and for n\leq…

We consider the classical geometric problem of prescribing the scalar and the boundary mean curvature in the unit ball endowed with the standard Euclidean metric. We will deal with the case of negative scalar curvature showing the existence…

In this paper, we give an explicit formula for the Futaki invariants of complete intersections. The result is new in the case where the variety is smooth or has orbifold singularities.

We consider the product of a compact Riemannian manifold without boundary and null scalar curvature with a compact Riemannian manifold with boundary, null scalar curvature and constant mean curvature on the boundary. We use bifurcation…

In the work of Ammann, Dahl and Humbert it has turned out that the Yamabe invariant on closed manifolds is a bordism invariant below a certain threshold constant. A similar result holds for a spinorial analogon. These threshold constants…

Assume that $(X, g^+)$ is an asymptotically hyperbolic manifold, $(M, [\bar{h}])$ is its conformal infinity, $\rho$ is the geodesic boundary defining function associated to $\bar{h}$ and $\bar{g} = \rho^2 g^+$. For any $\gamma \in (0,1)$,…

Formally self-adjoint, conformally covariant, polydifferential operators provide a general framework for studying variational problems, such as prescribing the scalar, $Q$-, or $\sigma_2$-curvatures, within a conformal class. We describe…

We prove the compactness of the set of solutions to the CR Yamabe problem on a compact strictly pseudoconvex CR manifold of dimension three whose blow-up manifolds at every point have positive p-mass. As a corollary we deduce that…

An octonionic contact (OC) manifold is always spherical. We construct the OC Yamabe operator on an OC manifold and prove its transformation formula under conformal OC transformations. An OC manifold is scalar positive, negative or vanishing…

We prove that in conformal classes of metrics near the class of an Einstein metric (other than the standard round metric on a sphere) the Yamabe problem has a unique solution up to scaling. This is a local extension, in the space of…

We obtain uncountably many periodic solutions to the singular Yamabe problem on a round sphere, that blow up along a great circle. These are (complete) constant scalar curvature metrics on the complement of $S^1$ inside $S^m$, $m\geq 5$,…

We prove existence of Yamabe metrics on four-manifolds possessing finitely-many conical points with $\mathbb{Z}_2$-group, using for the first time a min-max scheme in the singular setting. In our variational argument we need to deform…

We show that in an arbitrarily fixed conformal class on a closed manifold, the upper bound condition of the total scalar curvature is $C^{0}$-closed if its Yamabe constant is nonpositive. Moreover, we show that if a conformal class on a…