Related papers: Singular scalar curvature equations

Smooth Kahler-Einstein metrics have been studied for the past 80 years. More recently, singular Kahler-Einstein metrics have emerged as objects of intrinsic interest, both in differential and algebraic geometry, as well as a powerful tool…

We investigate degenerate special-Hermitian metrics on compact complex manifolds, in particular, degenerate K\"ahler and locally conformally K\"ahler metrics on special classes of non-K\"ahler manifolds.

We give sufficient conditions for the existence of Kaehler-Einstein and constant scalar curvature Kaehler (cscK) metrics on finite ramified Galois coverings of a cscK manifold in terms of cohomological conditions on the Kaehler classes and…

We derive a formula for the L^2 norm of the scalar curvature of any extremal Kaehler metric on a compact toric manifold, stated purely in terms of the geometry of the corresponding moment polytope. The main interest of this formula pertains…

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,…

In this paper, we propose a coupled system of complex Hessian equations which generalizes the equation for constant scalar curvature K\"ahler (cscK) metrics. We show this system can be realized variationally as the Euler-Lagrange equation…

We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics. We prove that a compact locally conformal K\"{a}hler manifold with constant nonpositive holomorphic sectional curvature is…

We prove the existence and uniqueness of the solutions of some very general type of degenerate complex Monge-Amp\`ere equations. This type of equations is precisely what is needed in order to construct K\"ahler-Einstein metrics over…

We survey some results on scalar curvature and properties of solutions to the Einstein constraint equations. Topics include an extended discussion of asymptotically flat solutions to the constraint equations, including recent results on the…

We prove that on one K\"{a}hler-Einstein Fano manifold without holomorphic vector fields, there exists a unique conical K\"{a}hler-Einstein metric along a simple normal crossing divisor with admissible prescribed cone angles. We also…

We relate certain universal curvature identities for Kaehler manifolds to the Euler-Lagrange equations of the scalar invariants which are defined by pairing characteristic forms with powers of the Kaehler form.

Motivated by the work of Li and Mantoulidis, we study singular metrics which are uniformly Euclidean $(L^\infty)$ on a compact manifold $M^n$ ($n\ge 3$) with negative Yamabe invariant $\sigma(M)$. It is well-known that if $g$ is a smooth…

Let $(X,L_X)$ be a polarized manifold and $D$ be a smooth hypersurface such that $D \in | L_X |$. In this paper, we show that if there is no nontrivial holomorphic vector field on $D$ and ${\rm Aut}_0 ((X,L_X); D)$ is trivial, then constant…

We construct a moduli space of polarised manifolds which admit a constant scalar curvature K\"ahler metric. We show that this space admits a natural K\"ahler metric.

Mechanical fields over thin elastic surfaces can develop singularities at isolated points and curves in response to constrained deformations (e.g., crumpling and folding of paper), singular body forces and couples, distributions of isolated…

In the first part we use Gromov's K--area to define the K--area homology which stabilizes into singular homology on the category of pairs of compact smooth manifolds. The second part treats the questions of certain curvature gaps. For…

We give an explicit formula for the quaternionic K\"ahler metrics obtained by the HK/QK correspondence. As an application, we give a new proof of the fact that the Ferrara-Sabharwal metric as well as its one-loop deformation is quaternionic…

In this short note, using the Kendall-Cranston coupling, we study on K\"ahler (resp. quaternion K\"ahler) manifolds first eigenvalue estimates in terms of dimension, diameter, and lower bounds on the holomorphic (resp. quaternionic)…

We give some estimate of type sup*inf for scalar curvature type equations.

Some curvature properties of Kahler manifolds of indefinite metrics are studied. Analogues of a Kulkarni's theorem are proved for such manifolds.