Asian Journal of Mathematics

Volume 22 (2018)

Number 3

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

DOI: https://dx.doi.org/10.4310/AJM.2018.v22.n3.a7

Authors

Morris Kalka (Department of Mathematics, Tulane University, New Orleans, Louisiana, U.S.A.)

Giorgio Patrizio (Dip. Matematica e Informatica, Università di Firenze, Italy; and Istituto Nazionale di Alta Matematica, Firenze, Italy)

Andrea Spiro (Scuola di Scienze e Tecnologie, Università di Camerino, Macerata, Italy)

Abstract

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.

Keywords

Monge–Ampère equations, almost homogenous manifolds, plurisuharmonic exhaustions, deformation of complex structures

2010 Mathematics Subject Classification

32M12, 32U10, 32W20

Full Text (PDF format)

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