References
M. Anderson, Ricci curvature bounds and Einstein metrics on compact manifolds, Jour. Amer. Math. Soc. 2 (1989), 455–490.
M. Anderson, Moduli spaces of Einstein metrics on 4-manifolds, Research Announ., Bull. Amer. Math. Soc. 21, No.2 (October 1989), 163–167.
M. Anderson, J. Cheeger, Diffeomorphism finiteness for manifolds with Ricci curvature andL n/2 norm of curvature bounded, Geometric and Functional Analysis 1, No. 3, (1991), 231–252.
S. Bando, Bubbling out of Einstein manifolds, Tohoku Math. Jour. 42, No. 2 (1990), 205–216; and 42, No. 4, 587–588.
S. Bando, A. Kasue, H. Nakajima, On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth, Invent. Math. 97 (1989), 313–349.
W. Barth, C. Peters, A. Van de Ven, Compact Complex Surfaces, Ergebnisse der Math. 3. Folge, Band 4, Springer Verlag, New York (1984).
A. Beauville, et al., Geometrie des surfaces K3: Modules et Periodes, Asterisque 126, Soc. Math. France (1983).
P. Berard, G. Besson, S. Gallot, Sur une inequalite isoperimetrique qui generalise celle de P. Levy-Gromov, Inventiones Math. 80 (1985), 295–308.
M. Berger, Une borne inferieure pour le volume d'une variete Riemannienne en fonction du rayon d'injectivite, Ann. Inst. Fourier, Grenoble, 30 (1980), 259–265.
L. Bers, Finite dimensional Teichmuller spaces and generalizations, Proc. Symp. Pure Math. 39:I (1983), 115–156.
A. Besse, Geometrie Riemannienne en Dimension 4, Cedic-Fernand Nathan Paris (1981).
A. Besse, Einstein Manifolds, Ergebnisse der Math., 3. Folge, Band 10, Springer Verlag, New York (1987).
D. Burns, M. Rapaport, On the Torelli problem for Kãhlerian K3 surfaces, Ann. Sci. Ecole Norm. Sup. IV, Serie 8 (1975), 235–274.
D. Burns, J. Wahl, Local contributions to global deformation of surfaces, Invent. Math. 26 (1974), 57–88.
J. Cheeger, M. Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded, II (II), Jour. Diff. Geom. 23 (1986), 309–346; and 32 (1990), 269–298.
J. Cheeger, M. Gromov, Chopping Riemannian manifolds, to appear in Do-Carmo Volume, Pitman Press.
C. Croke, Some isoperimetric inequalities and eigenvalue estimates, Ann. Sci. Ecole Norm. Sup. IV, Serie 13 (1980), 419–435.
D. Ebin, The manifold of Riemannian metrics, Proc. Symp. Pure Math. 15, Amer. Math. Soc. (1970), 11–40.
T. Eguchi, P. Gilkey, A. Hanson, Gravitation, Gauge Theories and Differential Geometry, Physical Reports 66 (1980), 213–393.
D. Freed, D. Groisser, The basic geometry of the manifold of Riemannian metrics and of its quotient by the diffeomorphism group, Mich. Math. Jour. 36 (1989), 323–344.
H. Federer, Geometric Measure Theory, Springer Verlag, New York (1969).
A. Fujiki, Kählerian normal complex spaces, Tohoku Math. Jour. 2nd Series 35 (1983), 101–118.
G. Gibbons, S. Hawking, Gravitational multi-instantons, Phys. Lett. B 78 (1978), 430–432.
M. Gromov, Structures Metriques pour les Varietes Riemanniennes, Cedic-Fernand Nathan, (1981).
M. Gromov, Paul Levy's isoperimetric inequality, Preprint, IHES (1979).
N. Hitchin, Polygons and gravitons, Math. Proc. Camb. Phil. Soc. 85 (1979), 465–476.
R. Kobayashi, Einstein-KählerV-metrics on open SatakeV-surfaces with isolated quotient singularities, Math. Ann. 272 (1985), 385–398.
R. Kobayashi, A. Todorov, Polarized period map for generalized K3 surfaces and the moduli of Einstein metrics, Tohoku Math. Jour. 39 (1987), 341–363.
N. Koiso, Rigidity and infinitesimal deformability of Einstein metrics, Osaka Jour. Math. 17 (1982), 643–668.
P. Kronheimer, The construction of ALE spaces as hyperkähler quotients, Jour. Diff. Geom. 29 (1989), 465–483.
D. Morrison, Some remarks on the moduli of K3 surfaces, Classification of Algebraic and Analytic Manifolds, Progress in Math., Birkhäuser Verlag 39 (1983), 303–332.
H. Nakajima, Hausdorff convergence of Einstein 4-manifolds, J. Fac. Sci. Univ. Tokyo 35 (1988), 411–424.
W. Rudin, Real and Complex Analysis, McGraw Hill, New York, (1977).
W. Thurston, The Geometry and Topology of 3-manifolds, (Preprint, Princeton).
G. Tian, Smoothness of the universal deformation space of compact Calabi-Yau manifolds and its Petersson-Weil metric, Mathematical Aspects of String Theory (ed. S.-T. Yau), World Scientific, Singapore (1987), 629–646.
G. Tian, On Calabi's conjecture for complex surfaces with positive first Chern class, Invent. Math. 101 (1990), 101–172.
G. Tian, S.-T. Yau, Kähler-Einstein metrics on complex surfaces withc 1>0, Comm. Math. Phys. 42 (1987), 175–203.
A. Todorov, Applications of the Kähler-Einstein-Calabi-Yau metric to moduli of K3 surfaces, Inventiones Math. 61 (1980), 251–265.
H. Tsuji, Existence and degeneration of Kähler-Einstein metrics on minimal algebraic varieties of general type, Math. Annalen 281 (1988), 123–133.
H. Wu, On manifolds of partially positive curvature, Indiana Univ. Math. Jour. 36, No.3 (1987), 525–548.
S.-T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampere equation, Comm. Pure and Appl. Math. 31 (1978), 339–441.
S.-T. Yau, Survey lecture, Seminar on Differential Geometry, Ann. of Math. Studies 102 (1982).
Author information
Authors and Affiliations
Additional information
Partially supported by NSF Grants DMS 87-01137 and 89-01303
Rights and permissions
About this article
Cite this article
Anderson, M.T. TheL 2 structure of moduli spaces of Einstein metrics on 4-manifolds. Geometric and Functional Analysis 2, 29–89 (1992). https://doi.org/10.1007/BF01895705
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01895705