Liang Cheng

activity

20232025

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math.DG2025

On the rigidity of manifolds with respect to Gagliardo-Nirenberg inequalities

Liang Cheng

In this paper, we investigate local rigidity properties related to Gagliardo-Nirenberg constants and unweighted Yamabe-type constants. Let $V$ be an open bounded subset of an $n$ -d…

math.DG2025

An $ε$ -regularity theorem for Perelman's reduced volume

Liang Cheng, Yongjia Zhang

In this article, we prove an $ε$ -regularity theorem for Perelman's reduced volume. We show that on a Ricci flow, if Perelman's reduced volume is close to $1$ , then the curvature ra…

On the rigidity of manifolds with respect to Gagliardo-Nirenberg inequalities

An ε-regularity theorem for Perelman's reduced volume

An $ε$ -regularity theorem for Perelman's reduced volume