Convergence and rigidity of manifolds under Ricci curvature bounds

Michael T. Anderson

Type: Article

Publication Date: 1990-12-01

Citations: 379

DOI: https://doi.org/10.1007/bf01233434

View Publication

Locations

Inventiones mathematicae - View

Similar Works

Action	Title	Year	Authors
+	Convergence of Riemannian 3-Manifolds Under a Ricci Curvature Bound	1994	Jyh-Yang Wu
+ PDF Chat	Rigidity Phenomena in Manifolds with Boundary Under a Lower Weighted Ricci Curvature Bound	2018	Yohei Sakurai
+	Rigidity of manifolds with Bakry–Émery Ricci curvature bounded below	2011	Yanhui Su Hui-Chun Zhang
+	Convergence and Regularity of Manifolds with Scalar Curvature and Entropy Lower Bounds	2023	Man-Chun Lee Aaron Naber Robin Neumayer
+ PDF Chat	Rigidity Theorems for Compact Manifolds with Boundary and Positive Ricci Curvature	2009	Fengbo Hang Xiaodong Wang
+ PDF Chat	A topological rigidity theorem on open manifolds with nonnegative Ricci curvature	2004	Qiaoling Wang
+	Rigidity and sphere theorem for manifolds with positive Ricci curvature	1994	Changyu Xia
+	Rigidity and finiteness under Ricci curvature and volume controls	2002	W.-H. Chen
+	Spaces with Ricci curvature bounds	1998	Tobias Colding
+	Convergence of Riemannian manifolds with critical curvature bounds	2017	Norman Zergänge
+ PDF Chat	The almost rigidity of manifolds with lower bounds on Ricci curvature and minimal volume growth	2000	Christina Sormani
+ PDF Chat	Rigidity of convex domains in manifolds with nonnegative Ricci and sectional curvature	1989	Viktor Schroeder Martin Strake
+ PDF Chat	Ricci Curvature Bounds and Einstein Metrics on Compact Manifolds	1989	Michael T. Anderson
+	On the spaces with Ricci curvature bounds	2019	Shouhei Honda
+	Ricci curvature and the topology of open manifolds	2012	Manfredo do Carmo Changyu Xia
+	Ricci curvature and the topology of open manifolds	2000	Manfredo do Carmo Changyu Xia
+	Curvature aspects of rigidity and flexibility of complex manifolds	2024
+	Rigidity of Surfaces with Constant Extrinsic Curvature in Riemannian Product Spaces	2020	Fábio R. dos Santos
+	Compactness of pseudohermitian structures with integral bounds on curvature	2005	Hung-Lin Chiu
+ PDF Chat	$C^\alpha$-compactness for manifolds with Ricci curvature and injectivity radius bounded below	1992	Michael T. Anderson Jeff Cheeger

Works That Cite This (375)

Action	Title	Year	Authors
+	Nilpotent structures and collapsing Ricci-flat metrics on the K3 surface	2021	Hans‐Joachim Hein Song Sun Jeff Viaclovsky Ruobing Zhang
+ PDF Chat	Manifolds of Ricci curvature and local rewinding volume bounded below	2018	Xiaochun Rong
+	MANIFOLDS WITH KILLING SPINORS AND PINCHING OF FIRST DIRAC EIGENVALUES	2007	Rheinischen Friedrich-Wilhelms-Universit
+	A sphere theorem for Bach-flat manifolds with positive constant scalar curvature	2019	Yi Fang Wei Yuan
+ PDF Chat	On the structure of Ricci shrinkers	2021	Haozhao Li Yu Li Wang Bing
+ PDF Chat	Higher order distance-like functions and Sobolev spaces	2022	Debora Impera Michele Rimoldi Giona Veronelli
+	Eigenvalue pinching on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:msup><mml:mrow><mml:mtext>spin</mml:mtext></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msup></mml:math> manifolds	2016	Saskia Roos
+ PDF Chat	On the structure of spaces with Ricci curvature bounded below. I	1997	Jeff Cheeger Tobias Colding
+ PDF Chat	Length of a shortest closed geodesic in manifolds of dimension four	2022	Nan Wu Zhifei Zhu
+	Regularity of Kähler–Ricci flows on Fano manifolds	2016	Gang Tian Zhenlei Zhang

Works Cited by This (23)

Action	Title	Year	Authors
+ PDF Chat	The splitting theorem for manifolds of nonnegative Ricci curvature	1971	Jeff Cheeger Detlef Gromoll
+ PDF Chat	Some isoperimetric inequalities and eigenvalue estimates	1980	Christopher B. Croke
+ PDF Chat	A convergence theorem for Riemannian manifolds and some applications	1989	Atsushi Kasue
+ PDF Chat	Some regularity theorems in riemannian geometry	1981	Dennis DeTurck Jerry L. Kazdan
+ PDF Chat	The topology of certain Riemannian manifolds with positive Ricci curvature	1983	Yoe Itokawa
+	Multiple Integrals in the Calculus of Variations	1966	Charles B. Morrey
+ PDF Chat	Convergence of Riemannian manifolds; Ricci and $L\sp {n/2}$-curvature pinching	1990	Laiyuan Gao
+	Lipschitz convergence of manifolds of positive Ricci curvature with large volume	1989	Takao Yamaguchi
+	TheL 2 structure of moduli spaces of Einstein metrics on 4-manifolds	1992	Michael T. Anderson
+ PDF Chat	Homotopy type finiteness theorems for certain precompact families of Riemannian manifolds	1988	Takao Yamaguchi