Precise analysis of semilinear elliptic equations on the hyperbolic space and application to conformal scalar curvature. (Analyse précisée d’équations semi-linéaires elliptiques sur l’espace hyperbolique et application à la courbure scalaire conforme.) (French) Zbl 0939.53026
In the hyperbolic space \(H^n(-1)\), with conformal metric \(H_0= \rho^{-2}E\), \(\rho(x)=(1-x^2)\), the author studies the equations \(\Delta\nu=(A-f)(1+ \nu)+(g-A)(1+\nu)^p\), \(\nu>-1\), \(A>0\), \(p>1\), \(\Delta\nu= e^\nu(f-A)+A\), with given functions \(f\) and \(g\), their solutions, existence, uniqueness regularity and geometric sense (see also [M. C. Leung, Int. J. Math. 4, 841-857 (1993; Zbl 0810.53032)] and [A. Ratto, Proc. of the workshop on differential geometry and topology, Alghero 1992, 214-243 (1993; Zbl 0885.53045)].
Reviewer: M.Rahula (Tartu)
MSC:
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 58J05 | Elliptic equations on manifolds, general theory |
| 35J70 | Degenerate elliptic equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
References:
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