@Article{JMS-58-145,
author = {Si , Cuifang and Xu , Shicheng},
title = {Rigidity for Einstein Manifolds under Bounded Covering Geometry},
journal = {Journal of Mathematical Study},
year = {2025},
volume = {58},
number = {2},
pages = {145--163},
abstract = {<p style="text-align: justify;">In this note, we prove three rigidity results for Einstein manifolds with
bounded covering geometry. (1) An almost flat manifold $(M,g)$ must be flat if it is
Einstein, i.e. ${\rm Ric}_g =λg$ for some real number $λ.$ (2) A compact Einstein manifold with
a non-vanishing and almost maximal volume entropy is hyperbolic. (3) A compact
Einstein manifold admitting a uniform local rewinding almost maximal volume is isometric to a space form.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v58n2.25.02},
url = {http://global-sci.org/intro/article_detail/jms/24207.html}
}