We study Hermitian metrics with constant Chern scalar curvature on a compact complex manifold. In the first part of the thesis, we prove a priori estimates for metrics of constant Chern scalar curvature on a compact complex manifold conditional on an upper bound on the entropy, extending a recent result by Chen-Cheng in the K\"ahler setting which was used to prove existence of constant scalar curvature K\"ahler metrics. In the second part of the thesis, we demonstrate a parabolic flow approach to proving existence of constant Chern scalar curvature metrics. Specifically, we study an analogue of the Calabi flow in the non-K\"ahler setting for compact Hermitian manifolds with vanishing first Bott-Chern class. We prove a priori estimates on the evolving metric and show that the flow exists as long as the Chern scalar curvature remains bounded. If the Chern scalar curvature remains uniformly bounded for all time, then the flow converges smoothly to the unique constant Chern scalar curvature metric in the $\partial\bar{\partial}-$class of the initial metric.

Creator

• Shen, Xi Sisi Sisi

DOI

• https://doi.org/10.21985/n2-rnwd-sh20

Subject

• Mathematics

Language

• en

Alternate Identifier

• etdadmin_upload_818179
• http://dissertations.umi.com/northwestern:15559

Keyword

• complex geometry
• differential geometry
• partial differential equations
• geometric analysis

Date created

• 2021-01-01

Resource type

• Dissertation

Rights statement

• In Copyright