Yi Li

Eigenvalues and entropies under the harmonic-Ricci flow

In this paper, the author discusses the eigenvalues and entropies under the harmonic-Ricci flow, which is the Ricci flow coupled with the harmonic map flow. We give an alternative proof of results for compact steady and expanding harmonic-Ricci breathers. In the second part, we derive some monotonicity formulas for eigenvalues of the Laplacian under the harmonic-Ricci flow. Finally, we obtain the first variation of the shrinker and expanding entropies of the harmonic-Ricci flow.

A priori estimates for Donaldson’s equation over compact Hermitian manifolds

In this paper we prove a priori estimates for Donaldson equation’s

Localization, Hurwitz Numbers and the Witten Conjecture

begin{aligned} omega wedge (chi +sqrt{-1}partial bar{partial }varphi )^{n-1} =e^{F}(chi +sqrt{-1}partial bar{partial }varphi )^{n}, end{aligned}

Li-Yau Estimates for a Nonlinear Parabolic Equation on Manifolds

ω∧(χ+-1∂∂¯φ)n-1=eF(χ+-1∂∂¯φ)n,over a compact complex manifold

Harnack estimates for a heat-type equation under the Ricci flow

X

Mabuchi and Aubin-Yau functionals over complex three-folds

X of complex dimension