arXiv research

Holomorphic handle attaching proves complex surface properties.

The paper introduces surface-complexity to measure 3-manifold complexity.

We study Bott-Chern cohomology on compact complex non-Kähler surfaces. In particular, we compute such a cohomology for compact complex surfaces in class $\text{VII}$ and for compact complex surfaces diffeomorphic to solvmanifolds.

Survey on rational curves on complex surfaces, highlighting different approaches.

Study of complex surfaces in a specific pseudo-Riemannian space.

The paper proves properties of complex surfaces and their curvature.

Study bi-Hermitian metrics on complex surfaces and solve geometric PDEs.

Study on complexity of systolic geodesics on Bolza surface.

Study connects two types of metrics on complex surfaces.

Paper classifies special slant surfaces with varying curvature.

We study the problem of existence of F-structures on compact complex surfaces, giving a complete classification modulo the gap in the classification of surfaces of class VII. We then use these results to study the minimal entropy problem for compact complex surfaces. For instance we prove that compact Kahler surfaces o…

In this article we study minimal flat Lorentzian surfaces in Lorentzian complex space forms. First we prove that, for minimal flat Lorentzian surfaces in a Lorentzian complex form, the equation of Ricci is a consequence of the equations of Gauss and Codazzi. Then we classify minimal flat Lorentzian surfaces in the Lore…

Study complex surfaces fibered over Teichmüller curves with Veech fibers.

Circle packings on translation surfaces are consistent across different surfaces.

Study Hodge-de Rham numbers for almost complex 4-manifolds, extending properties from complex surfaces.

Study models Ricci flow on complex surfaces, showing mixed behavior.

Constructs moduli spaces for complex affine and dilation surfaces.

Projective rigidity of circle packings on complex surfaces proved.

Stable generalized complex structures on certain surfaces are constant.

We construct examples of complex algebraic surfaces not admitting normal embeddings (in the sense of semialgebraic or subanalytic sets) with image a complex algebraic surface.

Constructs a family to handle unstable fibers on complex surfaces.

Acyclicity proven for curve complex on surfaces.

We define an invariant, which we call surface-complexity, of closed 3-manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting properties: it is subadditive under connected sum and finite-to-one on …

After a short summary of known results on surface-complexity of closed 3-manifolds, we will classify all closed orientable 3-manifolds with surface-complexity one.

In this paper we investigate surfaces in $\mathbb C P^2$ without complex points and characterize the minimal surfaces without complex points and the minimal Lagrangian surfaces by Ruh-Vilms type theorems. We also discuss the liftability of an immersion from a surface to $\mathbb C P^2$ into $S^5$ in Appendix A.

The paper proves the Singer conjecture for aspherical complex surfaces and refines Gromov's inequality.

We study almost complex surfaces in the nearly Kähler $S^3\times S^3$. We show that there is a local correspondence between almost complex surfaces and solutions of the H-surface equation introduced by Wente. We find a global holomorphic differential on every almost complex surface, and show that when this differentia…

We give a classification of compact solitons for the pluriclosed flow on complex surfaces. First, by exploiting results from the Kodaira classification of surfaces, we show that the complex surface underlying a soliton must be Kähler except for the possibility of steady solitons on minimal Hopf surfaces. Then, we const…

Study on PMC surfaces in complex space forms, linking biconservative and totally real properties.

Paper calculates L-invariant and L*-invariant for complex surface sums.

For any compact, connected, orientable, finite-type surface with marked points other than the sphere with three marked points, we construct a finite rigid set of its arc complex: a finite simplicial subcomplex of its arc complex such that any locally injective map of this set into the arc complex of another surface wit…

We classify the transitive, effective, holomorphic actions of connected complex Lie groups on complex surfaces.

This is a continuation of our previous paper [14]. In [14], we introduced the first Aeppli-Chern class on compact complex manifolds, and proved that the $(1,1)$ curvature form of the Levi-Civita connection represents the first Aeppli-Chern class which is a natural link between Riemannian geometry and complex geometry. …

We propose the study of a conformally invariant functional for surfaces of complex projective plane which is closely related to the classical Willmore functional. We show that minimal surfaces of complex projective plane are critical for this functional and construct some minima for it via the twistors spaces of comple…

Classifies fake surfaces up to complexity 5.

Simple proof for special surface classification.

Classifies meromorphic affine connections on complex surfaces.

Two related constructions are studied: (1) The diagonal complex $\mathcal{D}$ and its barycentric subdivision $\mathcal{BD}$ related to a \textit{punctured} oriented surface $F$ equipped with a number of labeled marked points. (2) The symmetric diagonal complex $\mathcal{D}^{inv}$ and its barycentric subdivision $\math…

Finite rigid sets found in surface curve complexes.

Complex analysis aids in studying minimal surfaces.

A rigid set in a curve complex of a surface is a subcomplex such that every locally injective simplicial map from the set into the curve complex is induced by a homeomorphism of the surface. In this paper, we find finite rigid sets in the curve complexes of connected non-orientable surfaces of genus $g$ with $n$ holes …

In this article, we consider Cayley deformations of a compact complex surface in a Calabi--Yau four-fold. We will study complex deformations of compact complex submanifolds of Calabi--Yau manifolds with a view to explaining why complex and Cayley deformations of a compact complex surface are the same. We in fact prove …

Smooth complex surfaces with triple intersections using differential geometry.

Division algorithm for surface group rings yields standard complexes and cohomological dimensions.

In this paper we prove that no complex surface of general type is diffeomorphic to a rational surface, thereby completing the smooth classification of rational surfaces and the proof of the Van de Ven conjecture on the smooth invariance of Kodaira dimension.

In this paper almost complex surfaces of the nearly Kähler $S^3\times S^3$ are studied in a systematic way. We show that on such a surface it is possible to define a global holomorphic differential, which is induced by an almost product structure on the nearly Kähler $S^3\times S^3$. We also find a correspondence betwe…

Finite rigid sets found in complex of curves for surfaces.

Study proves correspondence for special bundles on complex surfaces.