Asian Journal of Mathematics
Volume 22 (2018)
Special issue in honor of Ngaiming Mok (2 of 3)
Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University
Monge–Ampère exhaustions of almost homogeneous manifolds
Pages: 523 – 544
We consider three fundamental classes of compact almost homogenous manifolds and show that the complements of singular complex orbits in such manifolds are endowed with plurisubharmonic exhaustions satisfying complex homogeneous Monge–Ampère equations. This extends to a new family of mixed type examples various classical results on parabolic spaces and complexifications of symmetric spaces. Rigidity results on complex spaces modeled on such new examples are given.
Monge–Ampère equations, almost homogenous manifolds, plurisuharmonic exhaustions, deformation of complex structures
2010 Mathematics Subject Classification
32M12, 32U10, 32W20
This research was partially supported by the Project MIUR “Real and Complex Manifolds: Geometry, Topology and Harmonic Analysis” and by GNSAGA of INdAM.
Received 14 November 2016
Accepted 1 June 2017
Published 8 August 2018