arXiv subjects

Farnaz Ghanbari

Publications and source records attributed to Farnaz Ghanbari.

2 recordsLinked to original sources

arXiv2024

Kähler Immersions of ALE Kähler Manifolds into Complex Space Forms

In this article, we investigate the Kähler immersions of special Asymptotically Locally Euclidean (ALE) Kähler metrics into complex space forms. We provide a relation between Kähler immersions problem of these metrics and the sign of their mass. Our result shows that these metrics with positive mass do not admit a Kähler immersion into complex Euclidean space. Moreover, we also obtain that these metrics with any sign of mass cannot be Kähler immersed into complex hyperbolic space.

math.DG↗

arXiv2023

Collapsing of Mean Curvature Flow of Hypersurfaces to Complex Submanifolds

In this paper, we produce explicit examples of mean curvature flow of (2m-1)-dimensional submanifolds which converge to (2m-2)-dimensional submanifolds at a finite time. These examples are a special class of hyperspheres in $\mathbb{C}^{m}$ with a $U(m)$-invariant Kähler metrics. We first discuss the mean curvature flow problem and then investigate the type of singularities for them.

math.DG↗