Higher Lelong Numbers and Convex Geometry

We prove the reversed Alexandrov–Fenchel inequality for mixed Monge–Ampère masses of plurisubharmonic functions, which generalizes a result of Demailly and Pham. As applications to convex geometry, this gives a complex analytic proof of the reversed Alexandrov–Fenchel inequality for mixed covolumes,...

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Veröffentlicht in:The Journal of Geometric Analysis 2021-03, Vol.31 (3), p.2525-2539
Hauptverfasser: Kim, Dano, Rashkovskii, Alexander
Format: Artikel
Sprache:eng
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Zusammenfassung:We prove the reversed Alexandrov–Fenchel inequality for mixed Monge–Ampère masses of plurisubharmonic functions, which generalizes a result of Demailly and Pham. As applications to convex geometry, this gives a complex analytic proof of the reversed Alexandrov–Fenchel inequality for mixed covolumes, which generalizes recent results in convex geometry of Kaveh–Khovanskii, Khovanskii–Timorin, Milman–Rotem and Schneider on reversed (or complemented) Brunn–Minkowski and Alexandrov–Fenchel inequalities. Also for toric plurisubharmonic functions in the Cegrell class, we confirm Demailly’s conjecture on the convergence of higher Lelong numbers under the canonical approximation.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-020-00362-w