Three-manifolds with positive Ricci curvature

Richard S. Hamilton

Type: Article

Publication Date: 1982-01-01

Citations: 2901

DOI: https://doi.org/10.4310/jdg/1214436922

Abstract

The evolution equation 259 4. Solution for a short time 260 5. Evolution equations with an integrability condition 262 6. Weakly parabolic linear systems 265 7. Evolution of the curvature 273 8. Curvature in dimension three 276 9. Preserving positive Ricci curvature .27910.Pinching the eigenvalues 283 11.The gradient of the scalar curvature 286 12. Interpolation inequalities for tensors 291 13.Higher derivatives of the curvature .29414.Long time existence 296 15.Controlling R^/R^ 299 16.Estimating the normalized equation 300 17. Exponential convergence 301

Locations

Journal of Differential Geometry - View - PDF

Similar Works

Action	Title	Year	Authors
+	The Cross Curvature Flow of 3-manifolds with Negative Sectional Curvature	2003	Bennett Chow Richard S. Hamilton
+	Riemannian manifolds with non-negative Ricci curvature	1972	André Avez
+	Positive isotropic curvature and Ricci flow	2008	Huy The Nguyen
+ PDF Chat	Existence, lifespan, and transfer rate of Ricci flows on manifolds with small Ricci curvature	2017	Fei He
+	Existence, Lifespan and Transfer Rate of Ricci Flows on Manifolds with Small Ricci Curvature	2016	Fei He
+ PDF Chat	Ricci Flow of Regions with Curvature Bounded Below in Dimension Three	2017	Miles Simon
+ PDF Chat	The Cross Curvature Flow of 3-Manifolds with Negative Sectional Curvature	2004	Bennett Chow Richard S. Hamilton
+	Convergence of Riemannian 3-Manifolds Under a Ricci Curvature Bound	1994	Jyh-Yang Wu
+	Convergence of Ricci flows with bounded scalar curvature	2016	Richard H. Bamler
+	Convergence of Ricci flows with bounded scalar curvature	2016	Richard H. Bamler
+	Ricci curvature, radial curvature and large volume growth	2010	Guanghan Li Yi Shi Chuanxi Wu
+ PDF Chat	Convergence of Ricci flows with bounded scalar curvature	2018	Richard H. Bamler
+	Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds	2022	Alix Deruelle Felix Schulze Miles Simon
+ PDF Chat	Positive intermediate curvatures and Ricci flow	2024	David González-Álvaro Masoumeh Zarei
+	Non-Riemannian Curvatures	2001
+	THE RICCI FLOW ON COMPLETE THREE-MANIFOLDS	2000	Bing-Long Chen Xi-Ping Zhu
+ PDF Chat	A local curvature estimate for the Ricci flow	2016	Brett Kotschwar Ovidiu Munteanu Jiaping Wang
+	A local curvature estimate for the Ricci flow	2015	Brett Kotschwar Ovidiu Munteanu Jiaping Wang
+	Hamilton's Ricci Flow	2006	Bennett Chow Peng Lü Lei Ni
+	Three-manifolds of positive Ricci curvature	2004	Bennett Chow Dan Knopf

Works That Cite This (2741)

Action	Title	Year	Authors
+	Binary Data Matrix Theory	2022	Manouchehr Amiri
+ PDF Chat	От гармонических отображений к потокам Риччи на основе техники Бохнера	2019	И. А. Александрова И. А. Александрова Сергей Евгеньевич Степанов С. Е. Степанов Irina Tsyganok Irina Tsyganok
+	Bennet Chow: “Ricci Solitons in Low Dimensions”. AMS 2023, 339 pp	2024	Klaus Kröncke
+	On Ricci solitons with quarter-symmetric connection	2024	Mehraj Ahmad Lone Idrees Fayaz Harry
+	Flots géométriques d'ordre quatre et pincement intégral de la courbure	2012	Vincent Bour
+	Shape analysis in shape space	2012	Jing Hua Vahid Taimouri
+	Long time existence and bounded scalar curvature in the Ricci-harmonic flow	2015	Yi Li
+	Quantum theories and geometric topology: A chapter in physical mathematics	2014	Kishore Marathe
+	Some Solitons on Homogeneous Almost $$\alpha$$-Cosymplectic $$3$$-Manifolds and Harmonic Manifolds	2024	Naeem Ahmad Pundeer Paritosh Ghosh Harsh Shah Arindam Bhattacharyya
+ PDF Chat	Stability and instability of Ricci solitons	2014	Klaus Kröncke

Works Cited by This (6)

Action	Title	Year	Authors
+	Ricci curvature and einstein metrics	1981	J P Bourguignon
+	Comparison Theorems in Riemannian Geometry	2008	Jeff Cheeger David G. Ebin
+ PDF Chat	Spaces of constant curvature	2010	Joseph A. Wolf
+ PDF Chat	Harmonic Maps of Manifolds with Boundary	1975	Richard S. Hamilton
+	Harmonic Mappings of Riemannian Manifolds	1964	James Eells J. H. Sampson
+	The inverse function theorem of Nash and Moser	1982	Richard S. Hamilton