Interpolating between constrained Li–Yau and Chow–Hamilton Harnack inequalities for a nonlinear parabolic equation

We establish a one-parameter family of Harnack inequalities connecting the constrained trace Li–Yau differential Harnack inequality for a nonlinear parabolic equation to the constrained trace Chow–Hamilton Harnack inequality for this nonlinear equation with respect to evolving metrics related to the Ricci flow on a 2-dimensional closed manifold. This result can be regarded as a nonlinear version of the previous work of Y. Zheng and the author [J.-Y. Wu, Y. Zheng, Interpolating between constrained Li–Yau and Chow–Hamilton Harnack inequalities on a surface, Arch. Math., 94 (2010) 591–600].