【摘要】 考虑Ricci流方程配上一个带有位势项的共轭热方程所构成的方程组,利用曹晓冬给出的Harnack量,定义两个熵,证明它们非正且在上述方程组下是单调增,从而推广了PERELMAN、曹晓冬和HAM-ILTON等人的结果.更多还原

【Abstract】 The conjugate heat equation with potentials under Ricci flow is considered in the paper.Two entropies are defined by using Xiaodong Cao’s Harnack quantities.It is proved that they are non-positive and monotone increasing under the above system of equations.Hence,this generalizes the results of Perelman,Xiaodong Cao,Hamilton,etc.更多还原