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Noncompact $L_p$-Minkowski problems

Journal Article


Abstract


  • 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

    $p\neq1$.

Publication Date


  • 2018

Citation


  • Huang, Y., & Liu, J. (2018). Noncompact $L_p$-Minkowski problems. Retrieved from http://arxiv.org/abs/1812.03309v1

Web Of Science Accession Number


Abstract


  • 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

    $p\neq1$.

Publication Date


  • 2018

Citation


  • Huang, Y., & Liu, J. (2018). Noncompact $L_p$-Minkowski problems. Retrieved from http://arxiv.org/abs/1812.03309v1

Web Of Science Accession Number