Matrix Li–Yau–Hamilton estimates under Kähler–Ricci flow

Abstract

Click on the DOI link to access this article at the publishers website (may not be free).We prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Kähler–Ricci flow. These estimates are further extended to the constrained setting. As an application, we obtain a monotonicity formula. © Mathematica Josephina, Inc. 2025.Wichita State University, WSU; Division of Mathematical Sciences, DMS, (2405257); Division of Mathematical Sciences, DMS; National Science Foundation, NSF, (2316659); National Science Foundation, NSF; Simons Collaboration, (962228); National Natural Science Foundation of China, NSFC, (11571361); National Natural Science Foundation of China, NSFCXiaolong Li research is partially supported NSF-DMS #2405257, NSF LEAPS-MPS #2316659, Simons Collaboration Grant #962228, and a start-up grant at Wichita State University. Xin-An Ren research is partially supported by National Natural Science Foundation of China Grant #11571361