Surveys in Differential Geometry

Volume 26 (2021)

Introduction to a deformed Hermitian Yang–Mills flow

Pages: 157 – 168

DOI: https://dx.doi.org/10.4310/SDG.2021.v26.n1.a5

Authors

Jixiang Fu (Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China)

Shing-Tung Yau (Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)

Dekai Zhang (Department of Mathematics, Shanghai University, Shanghai, China)

Abstract

The deformed Hermitian Yang–Mills equation is an important fully nonlinear geometric PDE. In this survey, we sketch first some developments on the deformed Hermitian Yang–Mills equation, and then introduce a deformed Hermitian Yang–Mills flow. We present some results in our paper $\href{https://doi.org/10.1007/s40818-021-00100-7}{[9]}$ on this flow, including the longtime existence, the convergence under the subsolution condition, and as an application, the convergence on a Kähler surface case under the semisubsolution condition.

Full Text (PDF format)

Zhang would like to thank Prof. Xinan Ma for constant help and encouragement. Fu is supported by NSFC grant No. 12141104. Zhang is supported by NSFC grant No. 11901102.

Published 22 January 2024