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Matrix Li-Yau-Hamilton estimates under Ricci flow and parabolic frequency.

Xiaolong LiQi S Zhang
Published in: Calculus of variations and partial differential equations (2024)
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.
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