Monotonicity of functionals along conformal Ricci flow

  title={Monotonicity of functionals along conformal Ricci flow},
  author={Fengjiang Li and Peng Lu and Jian-hong Wang and Yu Zheng},
  journal={Proceedings of the American Mathematical Society},
The main purpose of this note is to construct two functionals of the positive solutions to the conjugate heat equation associated to the metrics evolving by the conformal Ricci flow on closed manifolds. We show that they are nondecreasing by calculating the explicit evolution formulas of these functionals. For the entropy functional we give another proof of the monotonicity by establishing a pointwise formula. Moreover, we show that the increase are strict unless the metrics are Einstein. 



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