On the existence of solutions to the Orlicz Aleksandrov problem

On the existence of solutions to the Orlicz Aleksandrov problem

In [Int Math Res Not 7: 5492–5519 (2021)], Feng and He introduced the Orlicz Aleksandrov problem and proved that, there exists a convex body and an explicit constant, such that the problem is solved provided the given measure is even. In this paper, extending their results, we first prove that the d...

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Veröffentlicht in:Geometriae dedicata 2023-06, Vol.217 (3), Article 57
Hauptverfasser: Hu, Zejun, Li, Hai
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
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Zusammenfassung:In [Int Math Res Not 7: 5492–5519 (2021)], Feng and He introduced the Orlicz Aleksandrov problem and proved that, there exists a convex body and an explicit constant, such that the problem is solved provided the given measure is even. In this paper, extending their results, we first prove that the desired convex body always exists for each constant in an interval. Then, we prove the existence of solutions to the problem for general measure that is not necessarily even.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-023-00794-y