Paper · Aug 10, 2021
Hessian estimates for the conjugate heat equation coupled with the Ricci flow
As on arXiv
Abstract
In this short note we obtain some local and global upper bounds for the Hessian of a positive solution to the conjugate heat equation coupled with the Ricci flow.
Comments: a preliminary note
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
-
Matrix Li-Yau-Hamilton Estimates under Kähler-Ricci Flow
Topics Heat kernel · Shared terms “conjugate heat”, “positive solutions”
-
Matrix Li-Yau-Hamilton estimates under Ricci Flow and parabolic frequency
Topics Heat kernel · Shared terms “conjugate heat”, “positive solutions”
-
Dynamical functionals on ancient ARF Ricci flows
Topics Heat kernel · Shared terms “conjugate heat”, “upper bound”
-
A direct approach to sharp Li-Yau Estimates on closed manifolds with negative Ricci lower bound
Topics Heat kernel · Shared terms “conjugate heat”, “positive solutions”
-
Scalar curvature, entropy, and generalized Ricci flow
Topics Heat kernel · Shared terms “conjugate heat”
-
An Anisotropic Entropy for the Rotationally Symmetric Ricci Flow
Topics Heat kernel · Shared terms “conjugate heat”
-
Heat kernel on Ricci shrinkers (II)
Topics Heat kernel
-
Sharp Gaussian Isoperimetry along a Ricci Flow
Topics Heat kernel · Shared terms “conjugate heat”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 6A.3The Heat Equation on ℝⁿ
The heat kernel, smoothing, uniqueness, Brownian motion, and a Gaussian that runs to Perelman.
- 6A.4Fourier Methods and Scale Space
Fourier's own method on the circle and the line, smoothing as the decay of high frequencies, and the heat equation as the mathematics of blurring images.
- 6A.12Entropy, Information and Diffusion
Entropy along the heat flow, the log-Sobolev inequality and Li–Yau: the ancestors of Perelman’s entropy.