A Construction of Non-K\"ahler Calabi-Yau Manifolds and New Solutions to the Strominger System

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 $\Sigma_g\times T^4$, where $\Sigma_g$ is an immersed minimal surface of genus $g\geq3$ in $T^3$.