As an example Existence of Hermitian-Einstein metric on stable Orbifold bundle on orbifolds which initial metric can be non-smooth in general. Or finding twisted Hermitian-Einstein metric on holomorphic fiber space needed to assume initial metric to be singular, see my question in MO. Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kahler-Einstein Metrics / Yum-Tong Siu / Introduction to Complex Analytic Geometry / Stanislaw Lojasiewicz / Laurent Series and Their Pade Approximation / Adhemar Bultheel / The Mathematical Sciences Research Institute (MSRI), founded in , is an independent nonprofit mathematical research institution whose funding sources include the National Science Foundation, foundations, corporations, and more than 90 universities and institutions. The Institute is located at 17 Gauss Way, on the University of California, Berkeley campus, close to Grizzly Peak, on the. Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share .

Limit behavior of metrics in K ahler{Einstein problem On the other hand, Ric(!) is the curvature form of the Hermitian line bundle K 1 M with Hermitian metric determined by . Preliminaries.- Kahler-Einstein metrics and extremal Kahler metrics.- The character f and its generalization to Kahlerian invariants.- The character f as an obstruction.- The character f as a classical invariant.- Lifting f to a group character.- The character f as a moment map.- Aubin's approach and related results. Series Title. We expand on the recent work of Demailly and Kollar [DK] and Johnson and Kollar [JK1] who give methods for constructing Kahler-Einstein metrics on log del Pezzo surfaces. By [BG1] circle V-bundles over log del Pezzo surfaces with Kahler-Einstein metrics have Sasakian-Einstein metrics on the total space of the bundle. AMS Chelsea Publishing: Comparison Theorems in Riemannian Geometry - Ebook written by Jeff Cheeger, D. G. Ebin. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read AMS Chelsea Publishing: Comparison Theorems in Riemannian Geometry.

Standard examples are the complete K\"ahler-Einstein metrics on bounded strictly pseudoconvex domains of $\mathbb{C}^n$ constructed by Cheng and Yau. If we want to obtain further such metrics, the natural idea is to deform the Cheng--Yau metrics, via analysis on the linearized Einstein operator acting on symmetric $2$-tensors.