Work

Continuous solutions to the quaternionic Monge-Ampère equation on locally flat HKT manifolds

Year: 2026

Type: preprint

Abstract: We prove that on a compact locally flat HKT manifold the quaternionic Monge--Ampère equation always has a unique continuous solution. This provides new evidence for the Conjecture of Alesker and Verbitsky.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.21528

Authors: Gentili, Giovanni, Trusiani, Antonio, Vezzoni, Luigi

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Agence Nationale de la Recherche, Fundação de Amparo à Pesquisa do Estado de São Paulo, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni

Awards: G1203447851, Brazil-France interplays in Gauge Theory, extremal structures and stability, G7606043282

OpenAlex ID: W7213886903

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