4 papers
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…
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 ra…
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…
On local rigidity theorems with respect to the scalar curvature
Liang Cheng
By using the Ricci flow, we study local rigidity theorems regarding scalar curvature, isoperimetric constant and best constant of logarithmic Sobolev inequality. Precisely, w…