TY - JOUR
T1 - The Monge–Ampère equation for (n-1)-quaternionic PSH functions on a hyperKähler manifold
AU - Fu, Jixiang
AU - Xu, Xin
AU - Zhang, Dekai
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
PY - 2024/6
Y1 - 2024/6
N2 - We prove the existence of a unique smooth solution to the quaternionic Monge–Ampère equation for (n-1)-quaternionic plurisubharmonic (psh) functions on a compact hyperKähler manifold and thus obtain solutions to the quaternionic form-type equation. We derive the C0 estimate by establishing a Cherrier-type inequality as in Tosatti and Weinkove (J Am Math Soc 30(2):311–346, 2017). By adopting the approach of Dinew and Sroka (Geom Funct Anal 33(4):875–911, 2023) to our context, we obtain the C1 and C2 estimates without assuming the flatness of underlying hyperKähler metric comparing to the previous result Gentili and Zhang (J Geom Anal 32:9, 2022).
AB - We prove the existence of a unique smooth solution to the quaternionic Monge–Ampère equation for (n-1)-quaternionic plurisubharmonic (psh) functions on a compact hyperKähler manifold and thus obtain solutions to the quaternionic form-type equation. We derive the C0 estimate by establishing a Cherrier-type inequality as in Tosatti and Weinkove (J Am Math Soc 30(2):311–346, 2017). By adopting the approach of Dinew and Sroka (Geom Funct Anal 33(4):875–911, 2023) to our context, we obtain the C1 and C2 estimates without assuming the flatness of underlying hyperKähler metric comparing to the previous result Gentili and Zhang (J Geom Anal 32:9, 2022).
UR - https://www.scopus.com/pages/publications/85192718828
U2 - 10.1007/s00209-024-03504-w
DO - 10.1007/s00209-024-03504-w
M3 - 文章
AN - SCOPUS:85192718828
SN - 0025-5874
VL - 307
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 2
M1 - 29
ER -