We prove uniform a priori estimates for degenerate complex Monge–Ampère equations on family of hermitian varieties. This generalizes theorem Di Nezza–Guedj–Guenancia to contexts. The main result can be applied study the boundedness Chern–Ricci flat potentials in conifold transitions.

In this work, we consider a class of Finsler metrics using the warped product notion introduced by Chen et al. [Internat. J. Math. 29 (2018), 1850081], with another “warping”, one that is consistent static spacetimes. We will give PDE characterization for proposed to be Ricci-flat and explicitly construct two non-Riemannian examples.

We prove the existence of a (unique) S-invariant Ricci-flat Kähler metric on a neighbourhood of the zero section in the canonical bundle of a realanalytic Kähler manifold X, extending the metric on X. In the important paper [3], Calabi proved existence of Ricci-flat Kähler metrics on two classes of manifolds: a) cotangent bundles of projective spaces; b) canonical bundles of Kähler-Einstein man...

We identify a set of “energy” functionals on the space of metrics in a given Kähler class on a Calabi-Yau manifold, that are bounded below and minimized uniquely on the Ricci-flat metric in that class. Using these functionals, we recast the problem of numerically solving the Einstein equation as an optimization problem. We test this strategy using the “algebraic” metrics (metrics for which the ...

At the leading order, the low-energy effective field equations in string theory admit solutions of the form of products of Minkowski spacetime and a Ricci-flat Calabi-Yau space. The equations of motion receive corrections at higher orders in α′, which imply that the Ricci-flat Calabi-Yau space is modified. In an appropriate choice of scheme, the Calabi-Yau space remains Kähler, but is no longer...