Tian's properness conjectures: an introduction to Kahler geometry
Differential Geometry
2024-11-21 v1 Analysis of PDEs
Complex Variables
Abstract
This manuscript served as lecture notes for a mini-course in the 2016 Southern California Geometric Analysis Seminar Winter School. The goal is to give a quick introduction to Kahler geometry by describing the recent resolution of Tian's three influential properness conjectures in joint work with T. Darvas. These results---inspired by and analogous to work on the Yamabe problem in conformal geometry---give an analytic characterization for the existence of Kahler--Einstein metrics and other important canonical metrics in complex geometry, as well as strong borderline Sobolev type inequalities referred to as the (strong) Moser--Trudinger inequalities.
Keywords
Cite
@article{arxiv.1807.00928,
title = {Tian's properness conjectures: an introduction to Kahler geometry},
author = {Yanir A. Rubinstein},
journal= {arXiv preprint arXiv:1807.00928},
year = {2024}
}