Related papers: K-stability and K\"ahler-Einstein metrics
We investigate compact complex manifolds endowed with SKT or balanced metrics. In each case we define a new functional whose critical points are proved to be precisely the K\"ahler metrics, if any, on the manifold. As general manifolds of…
This version corrects a number of mistakes that appeared in the previous draft. In particular, the (EU-LREM) condition is sufficient for existence and uniqueness but not necessary, as we had claimed. We are grateful to P. C. B. Phillips and…
This article corrects two mistakes in the article "Coarse homology theories" [math.AT/0106183].
We present an elementary way of recovering a well-known criterion of K-stability for Fano reductive group compactifications.
We discuss how metric limits and rescalings of K\"ahler-Einstein metrics connect with Algebraic Geometry, mostly in relation to the study of moduli spaces of varieties, and singularities. Along the way, we describe some elementary examples,…
We prove that existence of a k-rational point can be detected by the stable A^1-homotopy category of S^1-spectra, or even a "rationalized" variant of this category.
The purpose of this paper is to prove the uniqueness of conical K\"ahler-Einstein metrics, under the condition that the twisted $Ding$-functional is proper. This is a generalization of the author's previous work, and we shall first…
In this note, a modified K\"ahler-Ricci flow is introduced and studied. The main point is to show the flexibility of K\"ahler-Ricci flow and summarize some useful techniques.
This is a resubmission of preprint 9401008 , which has some TeXnical errors introduced by the "reform" procedure (designed to avoid precisely these problems!). The original can be formatted by editing out the messages "%% following line…
This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as…
In this note, we discuss a number of open problems in K-stability theory.
We study a variant of algebraic K-theory and prove that it is stable and preserves module structures.
In this note we correct two errors in our paper "On the Homology of Completion and Torsion", arXiv:1010.4386, that appeared in Algebras and Representation Theory (2014).
We construct explicit examples of quaternion-K\"ahler and hypercomplex structures on bundles over hyperK\"ahler manifolds. We study the infinitesimal symmetries of these examples and the associated Galicki-Lawson quaternion-K\"ahler moment…
In this paper we prove that for toric varieties the uniform K-stability is the necessary condition for the existence of extremal metrics.
We formulate a notion of K-stability for K\"ahler manifolds, and prove one direction of the Yau-Tian-Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi functional being bounded below (resp. coercive) implies…
Inspired by a parabolic system of Li-Yuan-Zhang and the continuity equation of La Nave-Tian, we study a system of elliptic equations for a K\"ahler metric $\omega$ and a closed $(1, 1)$-form $\alpha$. Assuming a uniform estimate for…
We introduce a cohomological obstruction to solving the constant scalar curvature K\"ahler (cscK) equation twisted by a semipositive form, appearing in works of Fine and Song-Tian. Geometrically this gives an obstruction for a manifold to…
We derive analogues of the classical Rayleigh, Fjortoft and Arnold stability and instability theorems in the context of the 2D $\alpha$-Euler equations.
In this paper we will investigate properties of modified q-Euler numbers and polynomials. The main purpose of this paper is to construct p-adic q-Euler measures.