3 papers
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 be an open bounded subset of an -d…
math.DG2025
The power series expansions of logarithmic Sobolev, - functionals and scalar curvature rigidity
Liang Cheng
In this paper, we obtain that the logarithmic Sobolev and -functionals admit remarkable power series expansions when appropriate test functions are selected. Using the…
math.DG2025
An -regularity theorem for Perelman's reduced volume
Liang Cheng, Yongjia Zhang
In this article, we prove an -regularity theorem for Perelman's reduced volume. We show that on a Ricci flow, if Perelman's reduced volume is close to , then the curvature r…