Asian Journal of Mathematics
Volume 22 (2018)
Special issue in honor of Ngaiming Mok (2 of 3)
Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University
On Harnack inequalities for Witten Laplacian on Riemannian manifolds with super Ricci flows
Pages: 577 – 598
In this paper, we prove the Li–Yau type Harnack inequality for the heat equation $\partial_t u = L u$ associated with the time-dependent Witten Laplacian on manifolds equipped with a variant of complete backward $(-K, m)$-super Perelman Ricci flows. Moreover, using a probabilistic approach we prove an improved Hamilton type Harnack inequality on manifolds equipped with complete $(-K)$-super Perelman Ricci flows.
Harnack inequality, super Perelman Ricci flows, Witten Laplacian
2010 Mathematics Subject Classification
Primary 58J35, 58J65. Secondary 60H30, 60J60.
Research supported by NSFC No. 11771430, Key Laboratory RCSDS, CAS, No. 2008DP173182, and by a Hua Luo-Keng Research Grant of the AMSS, CAS.
Received 31 October 2016
Accepted 7 June 2017
Published 8 August 2018