Results related to the Chern-Yamabe flow (Q2658996)

The author studies, for a compact complex manifold \(X\) of complex dimension \(n\), endowed with a Hermitian metric \(\omega_0\), the Chern-Yamabe problem, i.e., to find a conformal metric of \(\omega_0\) such that its Chern scalar curvature is constant. In this paper, as a generalisation of the Chern-Yamabe problem, the author focuses on the problem of prescribing Chern scalar curvature. The main results, with proofs (using geometric flows related to the Chern-Yamabe flow), are: \begin{itemize} \item[1] the estimation of the first non-zero eigenvalue of Hodge-de Rham Laplacian of \((X, \omega_0)\), \item[2] a proof of a version of conformal Schwarz lemma on \((X, \omega_0)\), \item[3] a proof of the uniqueness of the Chern-Yamabe flow. \end{itemize}