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Axioms
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Recent Advances in Complex Analysis and Applications, 2nd Edition
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Recent Advances in Complex Analysis and Applications, 2nd Edition

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (31 March 2026) | Viewed by 5876

Special Issue Editor

Prof. Dr. Miodrag Mateljevic

E-Mail Website
Guest Editor
Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 11000 Belgrade, Serbia
Interests: geometric function theory; harmonic maps; quasiconformal maps; Hardy spaces
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Complex numbers and complex analysis show up everywhere in mathematics and physics. This Special Issue, titled “Recent Advances in Complex Analysis and Applications II”, aims to provide a collection of high-quality original research articles and surveys in the field of Complex Analysis and Applications. Of particular interest are contributions addressing topics including, but not limited to, geometric function theory, quasiconformal harmonic maps, convex and starlike univalent functions, Lipschitz continuity and smoothness up to the boundary of solutions of the hyperbolic Poisson equation, spatial versions of Kellogg’s theorem, harmonic maps and maps which satisfy PDEs of second order, properties of mappings admitting general Poisson representations, Hardy spaces, extremal problems related to harmonic maps, etc.

Original articles reporting recent progress as well as survey articles are also welcome to be submitted to this Special Issue.

Prof. Dr. Miodrag Mateljevic
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • geometric function theory
  • harmonic maps
  • Hardy spaces
  • quasiconformal maps
  • univalent functions
  • harmonic analysis
  • PDE

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Published Papers (5 papers)

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Research

23 pages, 399 KB  
Article
Curvature–Cohomology Criterion for Projectivity: A Synthesis of Classical Results in Hodge Theory
by Ghaliah Alhamzi, Mona Bin-Asfour, Emad Solouma, Abdullah Alahmari, Mansoor Alsulami and Sayed Saber
Axioms 2026, 15(4), 265; https://doi.org/10.3390/axioms15040265 - 6 Apr 2026
Viewed by 401
Abstract
This paper synthesizes classical results in Hodge theory, curvature positivity, and vanishing theorems to give a concise curvature–cohomology criterion for the projectivity of compact Kähler manifolds. While each analytic component—Yau’s solution of the Calabi conjecture, the Bochner–Kodaira–Nakano identity, and Kodaira’s embedding theorem—is well-known, [...] Read more.
This paper synthesizes classical results in Hodge theory, curvature positivity, and vanishing theorems to give a concise curvature–cohomology criterion for the projectivity of compact Kähler manifolds. While each analytic component—Yau’s solution of the Calabi conjecture, the Bochner–Kodaira–Nakano identity, and Kodaira’s embedding theorem—is well-known, their combination yields a transparent geometric criterion: if the first Chern class c1(M) admits a semi-positive real (1,1) representative that is strictly positive at some point (or equivalently has a maximal rank n somewhere), then M is projective. Beyond the maximal rank case, we refine Girbau’s classical vanishing theorem to obtain an optimal rank-sensitive bound: if 2πc1(M) has a semi-positive representative whose pointwise rank is k somewhere, then Hp,0(M)=0 for all p>n−k. This sharpens the classical Girbau–Griffiths–Harris vanishing theorem and quantifies how partial positivity of a Ricci representative constrains Hodge cohomology. We situate these criteria alongside classical tests (Kodaira integrality and Moishezon) and numerical descriptions of the Kähler cone (Demailly–Paun), discuss deformation-invariance properties, and relate them to RC positivity and Campana–Peternell-type statements. Examples illustrate the sharpness of the hypotheses, and we survey the effective bounds—ranging from rigorous uniform high ampleness results to conjectural optimal constants—with clear distinction between proven theorems, refinements of classical results, and open problems. The contribution of this work lies not in new analytic techniques but in (1) isolating a sharp curvature condition at the level of c1(M); (2) organizing classical tools into a direct projectivity criterion; and (3) clarifying the rank-dependent vanishing behavior that follows from partial positivity. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications, 2nd Edition)
14 pages, 272 KB  
Article
Extremality of Koebe’s Function
by Samuel L. Krushkal
Axioms 2025, 14(12), 873; https://doi.org/10.3390/axioms14120873 - 28 Nov 2025
Cited by 3 | Viewed by 613
Abstract
The remarkable Koebe function is the (unique) extremal of many important distortion functionals in geometric function theory. This paper provides a complete characterization of such functionals. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications, 2nd Edition)
11 pages, 265 KB  
Article
On Certain Bounds of Harmonic Univalent Functions
by Fethiye Müge Sakar, Omendra Mishra, Georgia Irina Oros and Basem Aref Frasin
Axioms 2025, 14(6), 393; https://doi.org/10.3390/axioms14060393 - 22 May 2025
Cited by 1 | Viewed by 1493
Abstract
Harmonic functions are renowned for their application in the analysis of minimal surfaces. These functions are also very important in applied mathematics. Any harmonic function in the open unit disk U=z∈C:z<1 can be written as [...] Read more.
Harmonic functions are renowned for their application in the analysis of minimal surfaces. These functions are also very important in applied mathematics. Any harmonic function in the open unit disk U=z∈C:z<1 can be written as a sum f=h+g¯, where h and g are analytic functions in U and are called the analytic part and the co-analytic part of f, respectively. In this paper, the harmonic shear f=h+g¯∈SH and its rotation fμ by μμ∈C,μ=1 are considered. Bounds are established for this rotation fμ, specific inequalities that define the Jacobian of fμ are obtained, and the integral representation is determined. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications, 2nd Edition)
16 pages, 350 KB  
Article
Some Evaluations About Coefficients Boundaries for Specific Classes of Bi-Univalent Functions
by Suliman M. Sowileh, Gangadharan Murugusundaramoorthy, Borhen Halouani, Ibrahim S. Elshazly, Mohamed A. Mamon and Alaa H. El-Qadeem
Axioms 2024, 13(12), 821; https://doi.org/10.3390/axioms13120821 - 25 Nov 2024
Viewed by 978
Abstract
New subclasses of bi-univalent functions with bounded boundary rotation are presented in this study. We acquired estimates for the initial coefficients a2, a3 and a4. Furthermore, we have verified the specific situations satisfying the famous hypothesis of Brannan [...] Read more.
New subclasses of bi-univalent functions with bounded boundary rotation are presented in this study. We acquired estimates for the initial coefficients a2, a3 and a4. Furthermore, we have verified the specific situations satisfying the famous hypothesis of Brannan and Clunie. Additionally, we have obtained the well-known Fekete–Szegö inequality for the newly identified bi-univalent function subclasses. Our results not only improve, but also extend several existing results as particular cases. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications, 2nd Edition)
26 pages, 349 KB  
Article
Weighted Composition Operators between Bers-Type Spaces on Generalized Hua–Cartan–Hartogs Domains
by Ziyan Wang and Jianbing Su
Axioms 2024, 13(8), 513; https://doi.org/10.3390/axioms13080513 - 29 Jul 2024
Cited by 2 | Viewed by 1216
Abstract
We address weighted composition operators between Bers-type spaces on generalized Hua–Cartan–Hartogs domains and provide the necessary and sufficient conditions for their boundedness and compactness. We then apply our results to study the boundedness and the compactness of weighted composition operators between Bers-type spaces [...] Read more.
We address weighted composition operators between Bers-type spaces on generalized Hua–Cartan–Hartogs domains and provide the necessary and sufficient conditions for their boundedness and compactness. We then apply our results to study the boundedness and the compactness of weighted composition operators between Bers-type spaces on four different domains: generalized Hua domains, generalized Cartan–Hartogs domains, generalized Cartan–Hartogs domains over different Cartan domains and generalized ellipsoidal-type domains, by proving that the above four different domains are special cases of the generalized Hua–Cartan–Hartogs domains. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications, 2nd Edition)
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