2025 Theses Doctoral

On Curvature Estimate on Extended Kahler Ricci flow

Lee, Taeseok

In this paper, we introduced new version of extended Kähler Ricci Flow

𝜕𝑡𝜔=−Ric𝜔+𝛼_𝛰+𝛽_𝛰+ −1𝜕𝜕(1+𝑓)(1+𝒉)
𝜕𝑡 𝑓 = Δ𝜔 𝑓 + tr𝜔𝛼_𝛰
𝜕𝑡 𝒉 = Δ𝜔 𝒉 + tr𝜔 𝛼_𝛰

where 𝛰 is a Kähler metric, 𝑓, 𝒉 is a scalar function, and 𝛼_𝛰, 𝛽_𝛰 are closed (1,1) form. We first proved Shi-type curvature estimates and derivative estimates of simpler version on Riemann Surface. Then, we derive Shi-Type estimate on special case of 𝛼_𝛰 and 𝛽_𝛰. Therefore, the boundness of the curvature, 𝛼, 𝛽 and 𝐶² bound of 𝑓, 𝒉 implies the long existence of this flow.