Fully nonlinear elliptic equations for some prescribed curvature problems on Hermitian manifolds

2024/05/17 by Rirong Yuan, Yuan, Rirong · 1 citation
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2405.10771

Abstract

We study fully nonlinear elliptic equations on Hermitian manifolds through blow-up argument and partial uniform ellipticity. We apply our results to draw geometric conclusions on finding conformal Hermitian metrics with prescribed Chern-Ricci curvature functions. By some obstruction from geometric function theory, our assumptions are almost sharp.

Cited by

• Prescribed Chern scalar curvatures on complete Hermitian manifolds

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