L'équation de la chaleur associée à la courbure de Ricci
Séminaire Bourbaki (1985-1986)
- Volume: 28, page 45-61
- ISSN: 0303-1179
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topBourguignon, Jean Pierre. "L'équation de la chaleur associée à la courbure de Ricci." Séminaire Bourbaki 28 (1985-1986): 45-61. <http://eudml.org/doc/110070>.
@article{Bourguignon1985-1986,
author = {Bourguignon, Jean Pierre},
journal = {Séminaire Bourbaki},
keywords = {Four-manifolds with positive curvature operator; Ricci curvature; Riemannian metrics},
language = {fre},
pages = {45-61},
publisher = {Société Mathématique de France},
title = {L'équation de la chaleur associée à la courbure de Ricci},
url = {http://eudml.org/doc/110070},
volume = {28},
year = {1985-1986},
}
TY - JOUR
AU - Bourguignon, Jean Pierre
TI - L'équation de la chaleur associée à la courbure de Ricci
JO - Séminaire Bourbaki
PY - 1985-1986
PB - Société Mathématique de France
VL - 28
SP - 45
EP - 61
LA - fre
KW - Four-manifolds with positive curvature operator; Ricci curvature; Riemannian metrics
UR - http://eudml.org/doc/110070
ER -
References
top- [1] T. Aubin, Sur la courbure scalaire des variétés riemanniennes compactes, C. R. Acad. Sci. Paris262 (1966), 130-133. Zbl0139.39104MR195027
- [2] T. Aubin, Métriques riemanniennes et courbure, J. Differential Geom.4 (1970), 383-424. Zbl0212.54102MR279731
- [3] T. Aubin, Equations différentielles non linéaires et le problème de Yamabe concernant la courbure scalaire, J. Math. Pures Appl.55 (1976), 269-296. Zbl0336.53033MR431287
- [4] J. Bemelmans, M. Min'oo, E. Ruh, Smoothing Riemannian metrics, Preprint, Bonn University (1984). MR767363
- [5] P. Berard, The Bochner technique revisited, Preprint, Université de Savoie (1985).
- [6] A. Besse, Einstein manifolds, Ergebn. Math., Springer, Berlin-Heidelberg-New York, (1986). Zbl0613.53001MR867684
- [7] J.P. Bourguignon, L'espace des métriques riemanniennes d'une variété compacte, Thèse d'Etat, Université Paris VII (1974).
- [8] J.P. Bourguignon, Premières formes de Chern des variétés kählériennes compactes (d'après E. Calabi, T. Aubin et S.T. Yau), in Séminaire Bourbaki 1977-1978, Exposé n°507, Lecture Notes in Math. n°710, Springer, Berlin (1979), 1-21. Zbl0413.53035MR554212
- [9] J.P. Bourguignon, Ricci curvature and Einstein metrics, in Global Differential Geometry and Global Analysis, Lecture Notes in Math. n°838, Springer, Berlin (1981), 42-63. Zbl0437.53029MR636265
- [10] J.P. Bourguignon, H. Karcher, Curvature operators : pinching estimates and geometric examples, Ann. Sci. Ec. Norm. Sup. Paris11 (1978), 71-92. Zbl0386.53031MR493867
- [11] K.A. Brakke, The motion of a surface by its mean curvature, Math. Notes n°20, Princeton Univ. Press, Princeton (1978). Zbl0386.53047MR485012
- [12] D. Deturck, Existence of metrics with prescribed Ricci curvature : local theory, Inventiones Math.65 (1981), 179-207. Zbl0489.53014MR636886
- [13] D. Deturck, Deforming metrics in the direction of their Ricci tensors, J. Differential Geom.18 (1983), 157-162 ; idem : improved, to appear. Zbl0517.53044MR697987
- [14] D. Deturck, J.L. Kazdan, Some regularity theorems in Riemannian geometry, Ann. Sci. Ec. Norm. Sup. Paris14 (1981), 249-260. Zbl0486.53014MR644518
- [15] P. Dombrowski, 150 Years after Gauss' "Disquisitiones generales circa superficies curvas", Astérisque n°62 (1979). Zbl0406.01007MR535996
- [16] J. Eells, J.H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math.86 (1964), 109-160. Zbl0122.40102MR164306
- [17] P. Ehrlich, Metric deformations of curvature I : local convex deformations, Geom. Dedicata5 (1976), 1-23. Zbl0345.53024MR487886
- [18] P. Ehrlich, Metric deformations of curvature II : compact 3-manifolds, Geom. Dedicata5 (1976), 147-161. Zbl0364.53017MR487887
- [19] H. Eliasson, On variations of metrics, Math. Scand.29 (1971), 317-327. Zbl0238.53024MR312427
- [20] R.S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc.7 (1982), 65-222. Zbl0499.58003MR656198
- [21] R.S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom.17 (1982), 255-306. Zbl0504.53034MR664497
- [22] R.S. Hamilton, Four-manifolds with positive curvature operator, Preprint, U.C. San Diego (1985). MR862046
- [23] G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geom.20 (1984), 237-266. Zbl0556.53001MR772132
- [24] A. Inoue, On Yamabe's problem by a modified direct method, Tôhoku Math. J. (1982), 499-507. Zbl0533.53041MR685419
- [25] J.L. Kazdan, F. Warner, Prescribing curvatures, in Differential GeometryProc. Amer. Math. Soc. Symp. Pure Math.XXVII, Stanford (1975), 309-319. Zbl0313.53017MR394505
- [26] C. Margerin, Pointwise pinched manifolds are space forms, in Geometric measure theory, Amer. Math. Soc. Proc. Symp. Pure Math.44, Arcata (1985). Zbl0587.53042MR840282
- [27] M. Min'oo, E. Ruh, Curvature deformations, Preprint, Bonn University (1985). MR859584
- [28] G. Ricci-Curbastro, Direzioni e invarianti principali di una varietà qualunque, Atti Real Inst. Venezio, 63 (1904), 1233-1239. JFM35.0145.01
- [29] B. Riemann, Über die Hypothesen, welche der Geometrie zur Grunde liegen, in Gaussche Flächentheorie, Riemannsche Räume und Minkowski-Welt, Teubner-Archiv zur Mathematik, Band 1 (1984), 68-83.
- [30] E. Ruh, Riemannian manifolds with bounded curvature ratios, J. Differential Geom.17 (1982), 255-206. Zbl0508.53053MR683169
- [31] R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom.20 (1984), 479-495. Zbl0576.53028MR788292
- [32] R. Schoen, S.T. Yau, Complete 3-dimensional manifolds with positive Ricci curvature and scalar curvature, in Seminar on Differential Geometry, ed. by S.T. Yau, Ann. Math. Studies n°102, Princeton Univ. Press, Princeton (1982), 209-228. Zbl0481.53036MR645740
- [33] Séminaire Palaiseau1978, Première classe de Chern et courbure de Ricci : preuve de la conjecture de Calabi, Astérisque n°58 (1978). Zbl0397.35028
- [34] H. Yamabe, On a deformation of Riemannian structures on compact manifolds, Osaka J. Math.12 (1960), 21-37. Zbl0096.37201MR125546
- [35] S.T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation I, Comm. Pure Appl. Math.XXXI (1978), 339-411. Zbl0369.53059MR480350
Citations in EuDML Documents
top- Gérard Besson, Preuve de la conjecture de Poincaré en déformant la métrique par la courbure de Ricci
- G. Besson, On the Geometrisation Conjecture
- Jean-Pierre Bourguignon, Stabilité par déformation non-linéaire de la métrique de Minkowski
- Jean-Pierre Bourguignon, Métriques d'Einstein-Kähler sur les variétés de Fano : obstructions et existence
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