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The Journal of Geometric Analysis

, Volume 25, Issue 2, pp 783–819 | Cite as

Linear Trace Li–Yau–Hamilton Inequality for the CR Lichnerowicz–Laplacian Heat Equation

  • Shu-Cheng Chang
  • Ting-Hui ChangEmail author
  • Yen-Wen Fan
Article

Abstract

In this paper, we study the CR Lichnerowicz–Laplacian heat equation deformation of (1,1)-tensors on a complete strictly pseudoconvex CR (2n+1)-manifold. We derive the linear trace version of the Li–Yau–Hamilton inequality for positive solutions of the CR Lichnerowicz–Laplacian heat equation. We also obtain a nonlinear version of the Li–Yau–Hamilton inequality for the CR Lichnerowicz–Laplacian heat equation coupled with the CR Yamabe flow and trace Harnack inequality for the CR Yamabe flow.

Keywords

Li–Yau–Hamilton inequality Bochner–Weitzenböck formula CR Hodge–Laplacian CR Lichnerowicz–Laplacian heat equation CR Yamabe flow Torsion flow 

Mathematics Subject Classification

32V05 32V20 53C56 

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Copyright information

© Mathematica Josephina, Inc. 2013

Authors and Affiliations

  1. 1.Department of Mathematics and Taida Institute for Mathematical Sciences (TIMS)National Taiwan UniversityTaipeiTaiwan
  2. 2.Institute of MathematicsAcademia SinicaTaipeiTaiwan
  3. 3.Department of MathematicsNational Taiwan UniversityTaipeiTaiwan

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