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math.DG2022
Quantitative rigidity of almost maximal volume entropy for both RCD spaces and integral Ricci curvature bound
Lina Chen, Shicheng Xu
The volume entropy of a compact metric measure space is known to be the exponential growth rate of the measure lifted to its universal cover at infinity. For a compact Riemannian $…
math.DG2022
Almost maximal volume entropy rigidity for integral Ricci curvature in the non-collapsing case
Lina Chen
In this note we will show the almost maximal volume entropy rigidity for manifolds with lower integral Ricci curvature bound in the non-collapsing case: Given …
math.DG2022
Almost volume cone implies almost metric cone for annuluses centered at a compact set in -spaces
Lina Chen
In \cite{CC1}, Cheeger-Colding considered manifolds with lower Ricci curvature bound and gave some almost rigidity results about warped products including almost metric cone rigidi…