# zbMATH — the first resource for mathematics

Einstein metrics with prescribed conformal infinity on the ball. (English) Zbl 0765.53034
The authors prove the existence of an Einstein metric on a Euclidean ball of any dimension, realizing, as its conformal infinity, any prescribed metric on the boundary sphere which is sufficiently close (in a suitable Hölder topology) to the standard metric.

##### MSC:
 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
Full Text:
##### References:
 [1] Cheng, S.Y; Yau, S.T, Differential equations on Riemannian manifolds and their geometric applications, Comm. pure appl. math., 28, 333-354, (1975) · Zbl 0312.53031 [2] Cheng, S.Y; Yau, S.T, On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of Fefferman’s equation, Comm. pure appl. math, 33, 507-544, (1980) · Zbl 0506.53031 [3] DeTurck, D, Existence of metrics with prescribed Ricci curvature: local theory, Invent. math., 65, 179-207, (1981) · Zbl 0489.53014 [4] DeTurck, D, The Cauchy problem for Lorentz metrics with prescribed Ricci curvature, Compositio math., 48, 327-349, (1983) · Zbl 0527.53037 [5] Douglis, A; Nirenberg, L, Interior estimates for elliptic systems of partial differential equations, Comm. pure appl. math., 8, 503-538, (1955) · Zbl 0066.08002 [6] Fefferman, C; Graham, C.R, Conformal invariants, (), 95-116 [7] Gilbarg, D; Trudinger, N.S, Elliptic partial differential equations of second order, (1983), Springer-Verlag Berlin · Zbl 0691.35001 [8] LeBrun, C, $$H$$-space with a cosmological constant, (), 171-185 · Zbl 0549.53042 [9] Mazzeo, R.R, The Hodge cohomology of a conformally compact metric, J. differential geom., 28, 309-339, (1988) · Zbl 0656.53042 [10] Mazzeo, R.R; Melrose, R.B, Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature, J. funct. anal., 75, 260-310, (1987) · Zbl 0636.58034 [11] Melrose, R.B, Transformation of boundary problems, Acta math., 147, 149-236, (1981) · Zbl 0492.58023 [12] Morrey, C.B, Multiple integrals in the calculus of variations, (1966), Springer-Verlag Berlin · Zbl 0142.38701 [13] Pedersen, H, Einstein metrics, spinning top motions and monopoles, Math. ann., 274, 35-59, (1986) · Zbl 0566.53058 [14] Penrose, R; Rindler, W, () [15] Yau, S.-T, Harmonic functions on complete Riemannian manifolds, Comm. pure appl. math., 28, 201-228, (1975) · Zbl 0291.31002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.