We prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow. We then apply these estimates to establish the monotonicity of parabolic frequencies up to correction factors. As applications, we obtain some unique continuation results under the nonnegativity of sectional or complex sectional curvature.

中文翻译：

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里奇流和抛物线频率下的矩阵 Li-Yau-Hamilton 估计

我们证明了热方程和后向共轭热方程正解的矩阵 Li-Yau-Hamilton 估计，两者都与 Ricci 流耦合。然后，我们应用这些估计来建立抛物线频率的单调性直至校正因子。作为应用，我们在截面曲率或复截面曲率的非负性下得到了一些独特的连续结果。