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Noncompact $L_p$-Minkowski problems

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 نشر من قبل Jiakun Liu
 تاريخ النشر 2018
  مجال البحث
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In this paper we prove the existence of complete, noncompact convex hypersurfaces whose $p$-curvature function is prescribed on a domain in the unit sphere. This problem is related to the solvability of Monge-Amp`ere type equations subject to certain boundary conditions depending on the value of $p$. The special case of $p=1$ was previously studied by Pogorelov and Chou-Wang. Here, we give some sufficient conditions for the solvability for general $p eq1$.



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