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TITLE Results Related to the Chern-Yamabe Flow
KIAS AUTHORS Ho, Pak Tung
JOURNAL JOURNAL OF GEOMETRIC ANALYSIS, 2021
ARCHIVE  
ABSTRACT Let (X, omega(0)) be a compact complex manifold of complex dimension n endowed with a Hermitian metric omega(0). The Chern-Yamabe problem is to find a conformal metric of omega(0) such that its Chern scalar curvature is constant. As a generalization of the Chern-Yamabe problem, we study the problem of prescribing Chern scalar curvature. We then estimate the first nonzero eigenvalue of Hodge-de Rham Laplacian of (X, omega(0)). On the other hand, we prove a version of conformal Schwarz lemma on (X, omega(0)). All these are achieved by using geometric flows related to the Chern-Yamabe flow. Finally, we prove the backwards uniqueness of the Chern-Yamabe flow.
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