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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 $…
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 …
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…
Quantitative Volume Space From Rigidity with lower Ricci curvature bound II
Lina Chen, Xiaochun Rong, Shicheng Xu
This is the second paper of two in a series under the same title ([CRX]); both study the quantitative volume space form rigidity conjecture: a closed -manifold of Ricci curvatur…