The linear trace Harnack quadratic on a steady gradient Ricci soliton satisfies the heat equation
Bennett Chow, Peng Lu
TL;DR
This paper proves that the linear trace Harnack quadratic on steady and shrinking gradient Ricci solitons satisfies the heat equation, and explores connections between different Harnack inequalities.
Contribution
It establishes the heat equation property for the linear trace Harnack quadratic on steady and shrinker Ricci solitons and introduces an interpolation between two known Harnacks.
Findings
Linear trace Harnack quadratic satisfies the heat equation on steady solitons.
Similar property holds for shrinkers.
An interpolation between Perelman's and Cao--Hamilton's Harnacks is presented.
Abstract
We show that the linear trace Harnack quadratic on a steady gradient Ricci soliton satisfies the heat equation. Similar result holds for shrinkers. We also present an interpolation between Perelman's and Cao--Hamilton's Harnacks on a steady soliton.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds