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Noncompact lp-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-Ampère type equations subject to certain boundary conditions depending on the value of p. The special case of p = 1 was previously studied by Pogorelov [28] and Chou-Wang [10]. Here, we give some sufficient conditions for the solvability for general p . 1.

Publication Date


  • 2021

Citation


  • HUANG, Y., & LIU, J. (2021). Noncompact lp-minkowski problems. Indiana University Mathematics Journal, 70(3), 855-880. doi:10.1512/IUMJ.2021.70.8432

Scopus Eid


  • 2-s2.0-85110364245

Start Page


  • 855

End Page


  • 880

Volume


  • 70

Issue


  • 3

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-Ampère type equations subject to certain boundary conditions depending on the value of p. The special case of p = 1 was previously studied by Pogorelov [28] and Chou-Wang [10]. Here, we give some sufficient conditions for the solvability for general p . 1.

Publication Date


  • 2021

Citation


  • HUANG, Y., & LIU, J. (2021). Noncompact lp-minkowski problems. Indiana University Mathematics Journal, 70(3), 855-880. doi:10.1512/IUMJ.2021.70.8432

Scopus Eid


  • 2-s2.0-85110364245

Start Page


  • 855

End Page


  • 880

Volume


  • 70

Issue


  • 3