As on arXiv
Abstract
In this paper, we prove a Li-Yau-Hamilton type Harnack estimate for the -mean curvature flow in Euclidean space, which can be viewed as a gradient flow of the weighed area functional with the measure density function .
Comments: 11 pages
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.
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Monotonicity of Perelman -Entropy of Mean Curvature Flow
Topics Harnack inequalities · Same authors Xiang-Dong Li, Qi Yan · Shared terms “Hamilton”
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Topics Harnack inequalities · Shared terms “Hamilton”
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Topics Harnack inequalities · Shared terms “Hamilton”
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Topics Harnack inequalities · Same author Xiang-Dong Li · Shared terms “Yau Hamilton”
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Topics Harnack inequalities · Shared terms “type Harnack”
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Topics Mean curvature flow · Same authors Xiang-Dong Li, Qi Yan
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Topics Harnack inequalities
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Topics Harnack inequalities
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
- 6D.5Diffusions on Manifolds and Curvature
Brownian motion on a Riemannian manifold, the Bakry–Émery calculus, curvature-dimension inequalities, gradient estimates and log-Sobolev, coupling, and Brownian motion along a Ricci flow.
- 11B.2Ancient Solutions and the Harnack Inequality
Comparing curvature across space and time.
- 12A.6𝓛-Geodesics and the Variational Formulas
Perelman's §7.1 derived line by line: the first and second variation of 𝓛-length, 𝓛-Jacobi fields, adapted fields, Hamilton's Harnack expressions, and the differential inequalities for the reduced distance.