# $(1,1)$ forms with specified Lagrangian phase: a priori estimates and algebraic obstructions

@article{Collins201511FW,
title={\$(1,1)\$ forms with specified Lagrangian phase: a priori estimates and algebraic obstructions},
author={Tristan C. Collins and Adam Jacob and Shing-Tung Yau},
journal={arXiv: Differential Geometry},
year={2015}
}
• Published 2015
• Mathematics, Physics
• arXiv: Differential Geometry
Let $(X,\alpha)$ be a K\"ahler manifold of dimension n, and let $[\omega] \in H^{1,1}(X,\mathbb{R})$. We study the problem of specifying the Lagrangian phase of $\omega$ with respect to $\alpha$, which is described by the nonlinear elliptic equation $\sum_{i=1}^{n} \arctan(\lambda_i)= h(x)$ where $\lambda_i$ are the eigenvalues of $\omega$ with respect to $\alpha$. When $h(x)$ is a topological constant, this equation corresponds to the deformed Hermitian-Yang-Mills (dHYM) equation, and is… Expand
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