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A pointwise finite-dimensional reduction method for a fully coupled system of Einstein-Lichnerowicz type

par Premoselli, Bruno
Référence Communications in Contemporary Mathematics, 20, 6, 1750076
Publication Publié, 2018-09-01

Article révisé par les pairs

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Résumé :

We construct non-compactness examples for the fully coupled Einstein-Lichnerowicz constraint system in the focusing case. The construction is obtained by combining pointwise a priori asymptotic analysis techniques, finite-dimensional reductions and a fixed-point argument. More precisely, we perform a fixed-point procedure on the remainders of the expected blow-up decomposition. The argument consists of an involved finite-dimensional reduction coupled with a ping-pong method. To overcome the non-variational structure of the system, we work with remainders which belong to strong function spaces and not merely to energy spaces. Performing both the ping-pong argument and the finite-dimensional reduction therefore heavily relies on the a priori pointwise asymptotic techniques of the C0 theory.