Zobrazeno 1 - 10
of 146
pro vyhledávání: '"Viaclovsky, Jeff A."'
Autor:
Honda, Nobuhiro, Viaclovsky, Jeff
Let $Z$ be a compact, connected $3$-dimensional complex manifold with vanishing first and second Betti numbers and non-vanishing Euler characteristic. We prove that there is no holomorphic mapping from $Z$ onto any $2$-dimensional complex space. In o
Externí odkaz:
http://arxiv.org/abs/2403.05035
We prove Torelli-type uniqueness theorems for both ALG$^*$ gravitational instantons and ALG gravitational instantons which are of order $2$. That is, the periods uniquely characterize these types of gravitational instantons up to diffeomorphism. We d
Externí odkaz:
http://arxiv.org/abs/2112.07504
Autor:
Ju, Tao, Viaclovsky, Jeff
We study the prescribed scalar curvature problem in a conformal class on orbifolds with isolated singularities. We prove a compactness theorem in dimension $4$, and an existence theorem which holds in dimensions $n \geq 4$. This problem is more subtl
Externí odkaz:
http://arxiv.org/abs/2112.05207
We show that any asymptotically Calabi manifold which is Calabi-Yau can be compactified complex analytically to a weak Fano manifold. Furthermore, the Calabi-Yau structure arises from a generalized Tian-Yau construction on the compactification, and w
Externí odkaz:
http://arxiv.org/abs/2111.09287
Autor:
Chen, Gao, Viaclovsky, Jeff
There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type ALG and ALG$^*$. Gravitational instantons of type ALG were previously classified by Chen-Chen. In this paper, we prove a classification th
Externí odkaz:
http://arxiv.org/abs/2110.06498
We develop a Fredholm Theory for the Hodge Laplacian in weighted spaces on ALG$^*$ manifolds in dimension four. We then give several applications of this theory. First, we show the existence of harmonic functions with prescribed asymptotics at infini
Externí odkaz:
http://arxiv.org/abs/2109.08782
For any elliptic K3 surface $\mathfrak{F}: \mathcal{K} \rightarrow \mathbb{P}^1$, we construct a family of collapsing Ricci-flat K\"ahler metrics such that curvatures are uniformly bounded away from singular fibers, and which Gromov-Hausdorff limit t
Externí odkaz:
http://arxiv.org/abs/1910.11321
Autor:
Han, Jiyuan, Viaclovsky, Jeff A.
Publikováno v:
Forum of Mathematics, Sigma 8 (2020) e1
Our main result in this article is a compactness result which states that a noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat K\"ahler metrics on a minimal K\"ahler surface whose K\"ahler classes stay in a compact subset of
Externí odkaz:
http://arxiv.org/abs/1901.05611
Autor:
Han, Jiyuan, Viaclovsky, Jeff A.
In this article, we give a survey of our construction of a local moduli space of scalar-flat K\"ahler ALE metrics in complex dimension $2$. We also prove an explicit formula for the dimension of this moduli space on a scalar-flat K\"ahler ALE surface
Externí odkaz:
http://arxiv.org/abs/1809.07233
We exhibit families of Ricci-flat Kahler metrics on K3 surfaces which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding continuous surjective map from the K3 surface to the interval, with regul
Externí odkaz:
http://arxiv.org/abs/1807.09367