Minimal surfaces in Kähler surfaces and Ricci curvature

Ricci curvature, minimal surfaces and sphere theorems

Using an analogue of Myers’ theorem for minimal surfaces and three dimensional topology, we prove the diameter sphere theorem for Ricci curvature in dimension three and a corresponding eigenvalue pinching theorem. This settles these two problems for closed manifolds with positive Ricci curvature since they are both false in dimensions greater than three. §

Ricci Flow on Kähler-einstein Surfaces

0 Ricci flow on Kähler - Einstein surfaces

Digital cohomology groups of certain minimal surfaces

In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...

Kähler Surfaces And

A complex ruled surface admits an iterated blow-up encoded by a parabolic structure with rational weights. Under a condition of parabolic stability, one can construct a Kähler metric of constant scalar curvature on the blow-up according to [18]. We present a generalization of this construction to the case of parabolically polystable ruled surfaces. Thus we can produce numerous examples of Kähle...