Abstract
We consider the existence and regularity of maximizers (or minimizers) to two Monge-Ampere type functionals, one is the affine volume functional and the other arises in the study of Calabis extremal metrics on toric Kahler manifolds. The Euler equations of both functionals are fourth order partial differential equations, which are elliptic when the solution is a convex function. Both equations can be written as a system of a Monge-Ampere equation and a linearized Monge-Ampere equation. We discuss recent development on the regularity of maximizers to these two functionals
| Original language | English |
|---|---|
| Title of host publication | AMS/IP Studies in Advanced Mathematics, Fifth International Congress of Chinese Mathematicians Part 1 |
| Editors | Lizhen Ji |
| Place of Publication | United States of America |
| Publisher | International Press |
| Pages | 383-396pp |
| Volume | 51 |
| ISBN (Print) | 9780821875551 |
| Publication status | Published - 2012 |