scholarly journals Almost‐Rigidity of Frameworks

2020 ◽  
Author(s):  
Miranda Holmes‐Cerfon ◽  
Louis Theran ◽  
Steven J. Gortler
Keyword(s):  
Almost Rigidity

scholarly journals Almost-rigidity and the extinction time of positively curved Ricci flows

2016 ◽  
Vol 369 (1-2) ◽  
pp. 899-911 ◽  
Author(s):  
Richard H. Bamler ◽  
Davi Maximo
Keyword(s):  
Extinction Time ◽  
Ricci Flows ◽  
Positively Curved ◽  
Almost Rigidity

Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products

1996 ◽  
Vol 144 (1) ◽  
pp. 189 ◽  
Author(s):  
Jeff Cheeger ◽  
Tobias H. Colding
Keyword(s):  
Ricci Curvature ◽  
Lower Bounds ◽  
Warped Products ◽  
Almost Rigidity

scholarly journals An almost rigidity theorem and its applications to noncompact RCD(0,N) spaces with linear volume growth

2018 ◽  
Vol 22 (04) ◽  
pp. 1850076 ◽  
Author(s):  
Xian-Tao Huang
Keyword(s):  
Distance Function ◽  
Metric Space ◽  
Level Sets ◽  
Harmonic Functions ◽  
Polynomial Growth ◽  
Volume Growth ◽  
Rigidity Theorem ◽  
Existence Problem ◽  
Maximal Volume ◽  
Almost Rigidity

The main results of this paper consist of two parts. First, we obtain an almost rigidity theorem which roughly says that on an [Formula: see text] space, when a domain between two level sets of a distance function has almost maximal volume compared to that of a cylinder, then this portion is close to a cylinder as a metric space. Second, we apply this almost rigidity theorem to study noncompact [Formula: see text] spaces with linear volume growth. More precisely, we obtain the sublinear growth of diameter of geodesic spheres, and study the non-existence problem of nonconstant harmonic functions with polynomial growth on such [Formula: see text] spaces.

scholarly journals Segment Inequality and Almost Rigidity Structures for Integral Ricci Curvature

2021 ◽  
Author(s):  
Lina Chen
Keyword(s):  
Ricci Curvature ◽  
Hölder Continuity ◽  
Holder Continuity ◽  
Curvature Bound ◽  
Limit Space ◽  
Continuity Result ◽  
Segment Inequality ◽  
Almost Rigidity

Abstract We will show the Cheeger–Colding segment inequality for manifolds with integral Ricci curvature bound. By using this segment inequality, the almost rigidity structure results for integral Ricci curvature will be derived by a similar method as in [1]. And the sharp Hölder continuity result of [7] holds in the limit space of manifolds with integral Ricci curvature bound.

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