Related papers: The Fu-Yau equation in higher dimensions
In this paper, we study the Fu-Yau equation on compact Hermitian manifolds and prove the existence of solutions of equation on astheno-K\"ahler manifolds. We also prove the uniqueness of solutions of Fu-Yau equation when the slope parameter…
The Fu-Yau equation is an equation introduced by J. Fu and S.T. Yau as a generalization to arbitrary dimensions of an ansatz for the Strominger system. As in the Strominger system, it depends on a slope parameter $\alpha'$. The equation was…
We propose a new construction of compact non-K\"ahler Calabi-Yau manifolds with balanced metrics and study the Strominger system on them. In particular, we obtain explicit solutions to the Strominger system with degeneracies on…
In this paper we prove the existence and uniqueness of the form-type Calabi-Yau equation on K\"ahler manifolds of nonnegative orthogonal bisectional curvature.
In this paper we construct explicit smooth solutions to the Strominger system on generalized Calabi-Gray manifolds, which are compact non-K\"ahler Calabi-Yau 3-folds with infinitely many distinct topological types and sets of Hodge numbers.
In this paper, we study the following semilinear Schr\"odinger system $$ -\triangle u+u=(1+K_\alpha(\epsilon x))|u|^{p-2}u\ in \mathbb{R}^N, u\in H^1(\mathbb{R}^N) $$ where $3\leq p<2^*$ and $\epsilon>0$, $\alpha>0$ are small parameters.…
We solve the Fu-Yau equation for arbitrary dimension and arbitrary slope $\alpha'$. Actually we obtain at the same time a solution of the open case $\alpha'>0$, an improved solution of the known case $\alpha'<0$, and solutions for a family…
We study an equation proposed by Fu and Yau as a natural $n$-dimensional generalization of a Strominger system that they solved in dimension $2$. It is a complex Hessian equation with right hand side depending on gradients. Building on the…
In this paper we introduce a new equation on the compact Kahler manifolds. Solution of this equation corresponds to the Calabi-Yau metric. New equation differs from the Monge--Ampere equation considered by Calabi and Yau.
In this paper, we study the hypercritical deformed Hermitian-Yang-Mills equation on compact K\"ahler manifolds and resolve two conjectures of Collins-Yau.
We study the Strominger system with fixed balanced class. We show that classes which are the square of a K\"ahler metric admit solutions to the system for vector bundles satisfying the necessary conditions. Solutions are constructed by…
We construct solutions to the Strominger system on a class of noncompact Calabi-Yau 3-folds. These spaces include $\mathbb{C}^3$ and resolved conifold $\mathcal{O}(-1,-1)$ as special examples.
We continue our study of heterotic compactifications on non-Kahler complex manifolds with torsion. We give further evidence of the consistency of the six-dimensional manifold presented earlier and discuss the anomaly cancellation and…
In this paper, we extend a result of Gao Chen regarding the solvability of the twisted deformed Hermitian Yang-Mills equations on compact K\"ahler manifolds to allow for the twisting function to be non-constant and slightly negative in all…
We find a new obstruction to the existence of solutions of the Hull-Strominger system, which goes beyond the balanced property of the Calabi-Yau manifold $(X,\Omega)$ and the Mumford-Takemoto slope stability of the bundle over it. The basic…
We consider Calabi-Yau compactifications with one K\"ahler modulus. Following the method of Candelas et al. we use the mirror hypothesis to solve the quantum theory exactly in dependence of this modulus by performing the calculation for the…
Transversally K\"ahler foliations are a generalisation of K\"ahler manifolds, appearing naturally in the complex non-K\"ahler setting. We give a self-contained proof of how the classical methods used in the proof of the Aubin-Yau theorem…
We introduced a new flow to the LYZ equation on a compact K\"ahler manifold. We first show the existence of the longtime solution of the flow. We then show that under the Collins-Jacob-Yau's condition on the subsolution, the longtime…
In this paper we study the existence of solutions for a class of non-linear differential equation on compact Riemannian manifolds. We establish a lower and upper solutions' method to show the existence of a smooth positive solution for the…
We show that degenerate complex Monge-Ampere equations in a big cohomology class of a compact Kaehler manifold can be solved using a variational method independent of Yau's theorem. Our formulation yields in particular a natural…