Constant rank theorems are useful tools in geometric analysis for studying degeneracy and rigidity in nonlinear partial differential equations.

In this talk, we will discuss a quantitative constant rank theorem for positive semidefinite $(1,1)$-tensors on Hermitian manifolds, extending the result of Székelyhidi and Weinkove from the real setting.

We will explain the positivity and tensor conditions needed in this more general setting, together with the main ideas of the proof. As an application, we study the rank of the Ricci tensor on certain Hermitian manifolds. This part of the talk is based on previous work. If time permits, we will also discuss some recent developments in constant rank theorems and related questions.

 

Zoom Link

https://us02web.zoom.us/j/81026406803?pwd=exaO3PCdZCIAbTR1npi52kCbA9c2I8.1

 

Organizers

Siao-Hao Guo (NTU), Chao-Ming Lin (NTU), Wei-Bo Su (NCU), Chung-Jun Tsai (NTU)