Equations du type de Monge-Ampère sur les variétés Riemanniennes compactes,III |
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Authors: | Philippe Delanoe |
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Affiliation: | Département de Mathématiques, Université Pierre et Marie Curie, Paris, France |
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Abstract: | Let (Vn, g) be a C∞ compact Riemannian manifold without boundary. Given the following changes of metric: , where a is a fixed constant, we study the corresponding Monge-Ampère equations (1)±, (2)±. We first solve Eq. (2)?, under some simple assumptions on F?C∞. Then, using an appropriate change of functions that enables us to take advantage of the estimates just carried out for Eq. (2)?, we extend to Eq.(1)? all the results proved in our previous articles [5, 6] for the usual Monge-Ampère equation. Although equation (2)+ is not locally invertible, and does not even admit a solution for all , a similar change of functions leads to partial results about Eq. (1)+, via C2 and C3 estimates for Eq. (2)+. Eventually we give some comments and errata of our previous article (P. Delanoë, J. Funct. Anal.41 (1981), 341–353). |
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