{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SDLCW6SKWEABGQZEHF56SSBW7Z","short_pith_number":"pith:SDLCW6SK","schema_version":"1.0","canonical_sha256":"90d62b7a4ab100134324397be94836fe6f8b7fc64d92b19a0b583dc8c750611a","source":{"kind":"arxiv","id":"1401.0944","version":1},"attestation_state":"computed","paper":{"title":"Conformal metrics on $R^{2m}$ with constant Q-curvature, prescribed volume and asymptotic behavior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.DG","authors_text":"Ali Hyder, Luca Martinazzi","submitted_at":"2014-01-05T21:35:49Z","abstract_excerpt":"We study the solutions $u\\in C^\\infty(R^{2m})$ of the problem $(-\\Delta)^m u= Qe^{2mu}$, where $Q=\\pm (2m-1)!$, and $V :=\\int_{R^{2m}}e^{2mu}dx <\\infty$, particularly when $m>1$. This corresponds to finding conformal metrics $g_u:=e^{2u}|dx|^2$ on $R^{2m}$ with constant Q-curvature $Q$ and finite volume $V$. Extending previous works of Chang-Chen, and Wei-Ye, we show that both the value $V$ and the asymptotic behavior of $u(x)$ as $|x|\\to \\infty$ can be simultaneously prescribed, under certain restrictions. When $Q=(2m-1)!$ we need to assume $V1$. This corresponds to finding conformal metrics $g_u:=e^{2u}|dx|^2$ on $R^{2m}$ with constant Q-curvature $Q$ and finite volume $V$. Extending previous works of Chang-Chen, and Wei-Ye, we show that both the value $V$ and the asymptotic behavior of $u(x)$ as $|x|\\to \\infty$ can be simultaneously prescribed, under certain restrictions. When $Q=(2m-1)!$ we need to assume $V