arXiv 0810.05762008-10-03math.DG

Negativity of Perelman's Li-Yau-Hamilton type expression

Chengjie Yu

备注：: 4 pages

英文摘要：

Chau-Tam-Yu has proved the non-positivity of Perelman's new Li-Yau-Hamilton type expression on noncompact manifolds. In this article, we further prove that $v$ is negative if the Ricci flow is not end up with an Euclidean space.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Hamilton-Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture

In this paper, we provide an essentially self-contained and detailed account of the fundamental works of Hamilton and the recent breakthrough of Perelman on the Ricci flow and their application to the geometrization of three-manifolds. In particular, we give a detailed exposition of a complete proof of the Poincaré conjecture due to Hamilton and Perelman.

2006-12-03math.DG

A note on Perelman's LYH inequality

We give a proof to the Li-Yau-Hamilton type inequality claimed by Perelman on the fundamental solution to the conjugate heat equation. The rest of the paper is devoted to improving the known differential inequalities of Li-Yau-Hamilton type via monotonicity formulae.

2006-02-15math.DG

Thurston几何化猜想的Hamilton–Perelman证明的精简形式化

A Lean Formalization of the Hamilton--Perelman Proof of Thurston's Geometrization Conjecture

University of California San Diego（加州大学圣地亚哥分校）；Cornell University（康奈尔大学）；Princeton AI, Princeton University（普林斯顿大学人工智能实验室）；Tsinghua University（清华大学）；Amazon AGI（亚马逊AGI）；NVIDIA Research（英伟达研究）；University of Oregon（俄勒冈大学）

该研究对Thurston几何化猜想的Hamilton–Perelman Ricci流证明进行Lean形式化，重现公开Lean声明并记录验证，为几何化猜想的形式化验证提供支持。

2026-10-12math.DG

Hamilton–Perelman 三维庞加莱猜想证明的 Lean 形式化

A Lean Formalization of the Hamilton--Perelman Proof of the Three-Dimensional Poincaré Conjecture

Cornell University（康奈尔大学）；University of California San Diego（加州大学圣地亚哥分校）；Princeton Language and Intelligence, DaIS, Princeton University（普林斯顿语言智能与数据科学研究所，普林斯顿大学）；Department of Mathematics, University of California San Diego（加州大学圣地亚哥分校数学系）

本文用 Lean 形式化证明了三维庞加莱猜想，结合 Moise 定理，采用 Ricci 流与手术及有限时间消没的 Hamilton–Perelman 方法。

2026-09-29math.DG

The Wasserstein geometry of non-linear sigma models and the Hamilton-Perelman Ricci flow

Non linear sigma models are quantum field theories describing, in the large deviations sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton-Perelman Ricci flow. By exploiting the heat kernel embedding introduced by N. Gigli and C. Mantegazza, we show that the Wasserstein geometry of the space of probability measures over Riemannian metric measure spaces provides a natural setting for discussing the relation between non-linear sigma m…

2014-05-05math-phmath.DGmath.MP

A new Li-Yau-Hamilton estimate for Kahler-Ricci flow

In this paper we prove a new matrix Li-Yau-Hamilton estimate for Kähler-Ricci flow. The form of this new Li-Yau-Hamilton estimate is obtained by the interpolation consideration originated in \cite{Ch1}. This new inequality is shown to be connected with Perelman's entropy formula through a family of differential equalities. In the rest of the paper, We show several applications of this new estimate and its linear version proved earlier in \cite{CN}. These include a sharp heat kernel comparison theorem, generalizing the earlier result of Li and Tian, a manifold version of Stoll's theorem on the …

2005-04-04math.DG

更多相关论文收起更多论文

紧型对称空间上Perelman $\ u$-熵的线性稳定性

Linear stability of Perelman's $ν$-entropy on symmetric spaces of compact type

该文研究正Ricci曲率Einstein流形上Perelman $\ u$-熵的线性稳定性，证明其横向无迹对称2张量上的线性稳定性与Einstein流形关于Hilbert作用的稳定性等价，并完整分类了紧型对称空间上的该稳定性，给出了更多相关实例。

2013-04-09math.DG

Hamilton type entropy formula along the Ricci flow on surfaces with boundary

In this article, we establish a monotonicity formula of Hamilton type entropy along Ricci flow on compact surfaces with boundary. We also study the relation between our entropy functional and the $\mathcal{W}$-functional of Perelman type.

2021-07-07math.DG

On Harnack inequalities for Witten Laplacian on Riemannian manifolds with super Ricci flows

In this paper, we prove the Li-Yau type Harnack inequality and Hamilton type dimension free Harnack inequality for the heat equation $\partial_t u=Lu$ associated with the time dependent Witten Laplacian on complete Riemannian manifolds equipped with a variant of the $(K, m)$-super Perelman Ricci flows and the $K$-super Perelman Ricci flows.

2017-06-16math.DG

Some results for the Perelman LYH-type inequality

Let $(M,g(t))$, $0\le t\le T$, $\partial M\neϕ$, be a compact $n$-dimensional manifold, $n\ge 2$, with metric $g(t)$ evolving by the Ricci flow such that the second fundamental form of $\partial M$ with respect to the unit outward normal of $\partial M$ is uniformly bounded below on $\partial M\times [0,T]$. We will prove a global Li-Yau gradient estimate for the solution of the generalized conjugate heat equation on $M\times [0,T]$. We will give another proof of Perelman's Li-Yau-Hamilton type inequality for the fundamental solution of the conjugate heat equation on closed manifolds without u…

2008-05-12math.APmath.DG

Entropy Functionals, Sobolev Inequalities and kappa-Noncollapsing Estimates along the Ricci Flow

In this survey we review Hamilton's entropy and Perelman's entropy, and provide motivations for these concepts. Then we review recent results on the logarithmic Sobolev inequality, the Sobolev inequalities and kappa-noncollapsing estimates along the Ricci flow, including the Ricci flow with surgeries.

2007-09-18math.DG

卡拉比-丘流形上几何正性与负性的拓扑障碍

Topological obstructions to geometric positivity and negativity on Calabi-Yau manifolds

Fudan University（复旦大学）

该研究证明卡拉比-丘流形在特定维数下不同胚于弱Fano簇，其基本群不同构于凯勒双曲流形的基本群，揭示了其与几何正性/负性类的拓扑刚性差异。

2026-08-14math.AGmath.DGmath.SG