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Complex Monge-Ampère equations on Hermitian Manifolds: From bounded to smooth solutions
Abstract
We study regularity of bounded weak solutions to complex Monge-Amp{è}re equations on compact Hermitian manifolds with right-hand side possibly decreasing in the unknown. Our proof relies on the domination principle and a priori estimates, partially motivated by the Monge-Amp{è}re eigenvalue problem. Our main result roughly says that any bounded solution is smooth in the regular locus of the data. When the right-hand side is strictly positive and smooth, we recover known results by Nie, Ko lodziej-Nguyen for the Hermitian case and Sz{é}kelyhidi-Tosatti for the K{ä}hler case, which rely on the regularizing property of the K{ä}hler-Ricci flow.
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BibTeX
@misc{badiane2026complex,
title = {{Complex Monge-Ampère equations on Hermitian Manifolds: From bounded to smooth solutions}},
author = {Papa Badiane and Chinh H. Lu and Ahmed Zeriahi},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06473},
eprint = {2610.06473},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05776079v1},
}
RIS
TY - UNPB
TI - Complex Monge-Ampère equations on Hermitian Manifolds: From bounded to smooth solutions
AU - Papa Badiane
AU - Chinh H. Lu
AU - Ahmed Zeriahi
PY - 2026
DA - 2026/10/02
PB - HAL
DO - 10.48550/arxiv.2610.06473
UR - https://hal.science/hal-05776079v1
AB - We study regularity of bounded weak solutions to complex Monge-Amp{è}re equations on compact Hermitian manifolds with right-hand side possibly decreasing in the unknown. Our proof relies on the domination principle and a priori estimates, partially motivated by the Monge-Amp{è}re eigenvalue problem. Our main result roughly says that any bounded solution is smooth in the regular locus of the data. When the right-hand side is strictly positive and smooth, we recover known results by Nie, Ko lodziej-Nguyen for the Hermitian case and Sz{é}kelyhidi-Tosatti for the K{ä}hler case, which rely on the regularizing property of the K{ä}hler-Ricci flow.
ER -