PreprintCC0arXiv
Continuous solutions to the quaternionic Monge-Ampère equation on locally flat HKT manifolds
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.
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BibTeX
@misc{gentili2026continuous,
title = {{Continuous solutions to the quaternionic Monge-Ampère equation on locally flat HKT manifolds}},
author = {Giovanni Gentili and Antonio Trusiani and Luigi Vezzoni},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21528},
eprint = {2609.21528},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21528},
note = {CC0},
}
RIS
TY - UNPB
TI - Continuous solutions to the quaternionic Monge-Ampère equation on locally flat HKT manifolds
AU - Giovanni Gentili
AU - Antonio Trusiani
AU - Luigi Vezzoni
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21528
UR - https://arxiv.org/abs/2609.21528
AB - 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.
ER -