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Local $C^0$-estimate and existence theorems for some prescribed curvature problems on complete noncompact Riemannian manifolds

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 نشر من قبل Rirong Yuan
 تاريخ النشر 2021
  مجال البحث
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 تأليف Rirong Yuan




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In this article we study a class of prescribed curvature problems on complete noncompact Riemannian manifolds. To be precise, we derive local $C^0$-estimate under an asymptotic condition which is in effect optimal, and prove the existence of complete conformal metrics with prescribed curvature functions. A key ingredient of our strategy is Aviles-McOwens result or its fully nonlinear version on the existence of complete conformal metrics with prescribed curvature functions on manifolds with boundary.



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