Asian Journal of Mathematics
Volume 22 (2018)
Special issue in honor of Ngaiming Mok (1 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
CR Li–Yau gradient estimate for Witten Laplacian via Bakry–Emery pseudohermitian Ricci curvature
Pages: 223 – 256
In this paper, we derive the sub-gradient estimate of the CR heat equation associated with the Witten sub-Laplacian via the Bakry–Emery pseudohermitian Ricci curvature. With its applications, we first get a Harnack inequality for the positive solution of this CR heat equation in a closed pseudohermitian $(2n + 1)$-manifold. Secondly, we obtain Perelman-type linear entropy formulae for this CR heat equation.
CR heat equation, Li–Yau gradient estimate, Harnack inequality, Perelman entropy formulae, Bakry–Emery pseudohermitian Ricci curvature, Pseudohermitian manifold, Witten Laplacian
2010 Mathematics Subject Classification
Primary 32V05, 32V20. Secondary 53C56.
Received 15 October 2016
Accepted 15 June 2017
Published 15 June 2018