Duong H. PhongColumbia UniversitySebastien PicardUniversity of British ColumbiaXiangwen ZhangUniversity of California, Irvine
Analysis of PDEsComplex Variables and Complex AnalysisDifferential Geometrymathscidoc:2106.03001
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 of Hessian equations which includes the Fu-Yau equation as a special case. The method is based on the introduction of a more stringent ellipticity condition than the usual $\Gamma_k$ admissible cone condition, and which can be shown to be preserved by precise estimates with scale.