Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1910.02531

Kähler manifolds with almost non-negative curvature

Man-Chun Lee·Luen-Fai Tam
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, we construct local and global solutions to the Kähler-Ricci flow from a non-collapsed Kähler manifold with curvature bounded from below. Combines with the mollification technique of McLeod-Simon-Topping, we show that the Gromov-Hausdorff limit of sequence of complete noncompact non-collapsed Kähler manifolds with orthogonal bisectional curvature and Ricci curvature bounded from below is homeomorphic to a complex manifold. We also use it to study the complex structure of complete Kähler manifolds with nonnegative orthogonal bisectional curvature, nonnegative Ricci curvature and maximal volume growth.

Explore related subjects

math.DGmath.CV

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Man-Chun Lee, Luen-Fai Tam. 2020-11-04. Kähler manifolds with almost non-negative curvature. https://doi.org/10.2140/gt.2021.25.1979

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Futaki invariant on Hopf manifolds

The Futaki invariant is a fundamental tool in Kähler geometry representing an obstruction to the existence of Kähler-Einstein metrics. Recently, it was generalized to compact complex manifolds. In this paper, we prove that it vanishes on Hopf manifolds.

math.DG↗
arXiv2026

Remarks on potential functions of noncompact quasi-Einstein manifolds

In this article, we study the set of potential functions on noncompact quasi-Einstein manifolds. We show that the space of all positive potential functions on a three-dimensional noncompact quasi-Einstein manifold has dimension at most two, and that equality holds if and only if the manifold is isometric to a product $B\times\mathbb{R}$, where $B$ is a $λ$-Einstein surface or one of the examples obtained by L. Berard Bergery and described in Besse's book. Moreover, we prove that any asymptotically flat $n$-dimensional quasi-Einstein manifold with $λ=0$ is necessarily Ricci-flat.

math.DG↗
arXiv2026

Adjusted connections on non-abelian bundle gerbes

Higher gauge theory for non-abelian structure 2-groups faces significant challenges when extending beyond the fake-flat sector, which suffers from limited applicability in physical models. A promising resolution involves equipping 2-groups with additional structure, known as adjustments. We present a comprehensive theory of adjusted connections on non-abelian bundle gerbes, classified by Saemann's adjusted version of non-abelian differential cohomology. This theory enables, in particular, a new coordinate-independent formulation of Tellez-Dominguez' lifting theorem, establishing a correspondence between adjusted connections on non-abelian bundle gerbes and connections on abelian bundle 2-gerbes.

math.DG↗