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Topic · Geometry and Topology

Analytic and geometric function theory

Analytic and geometric function theory is a research topic within Geometry and Topology. Science Explorer counts 13k research works in it since 1950. 10.2% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the study of geometric function theory and complex analysis, particularly on topics such as analytic and univalent functions, conformal and quasiconformal mappings, coefficient estimates, subordination, and harmonic mappings. It also explores the applications of hypergeometric functions in this context.

  • Geometric Function Theory
  • Complex Analysis
  • Analytic Functions
  • Univalent Functions
  • Conformal Mapping
  • Coefficient Estimates
  • Subordination
  • Harmonic Mappings
  • Quasiconformal Mappings
  • Hypergeometric Functions
Research works
13k
fractional, since 1950
In the world top 10%
1.3k
per year above
Top-10% rate
10.2%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+9%
the tick is no change
Largest producer
India
19% of the 10 largest, 2022-now
Analytic and geometric function theory

Which countries lead Analytic and geometric function theory research?

By volume, India and China publish the most (286 and 263 works in 2022-now).

By volume, 2022-now

  1. 1 India 286 works
  2. 2 China 263 works
  3. 3 United States 177 works
  4. 4 Russia 137 works
  5. 5 Iraq 132 works
  6. 6 Türkiye 111 works
  7. 7 Saudi Arabia 108 works
  8. 8 Romania 105 works
  9. 9 Ukraine 85 works
  10. 10 Pakistan 68 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

India: 19.4%China: 17.8%United States: 12.0%Russia: 9.3%6 others listed: 41.4%19%largest
India286 · 19.4%China263 · 17.8%United States177 · 12.0%Russia137 · 9.3%6 others listed610 · 41.4%

Shares of the rows listed above, not of the whole node.

Which institutions lead Analytic and geometric function theory research?

By volume in 2022-now, University of Al-Qadisiyah publishes the most Analytic and geometric function theory research, followed by Russian Academy of Sciences and University of Oradea.

By volume, 2022-now

  1. 1 University of Al-QadisiyahIraq 51 works
  2. 2 Russian Academy of SciencesRussia 46 works
  3. 3 University of OradeaRomania 38 works
  4. 4 National Academy of Sciences of UkraineUkraine 30 works
  5. 5 Vellore Institute of Technology UniversityIndia 24 works
  6. 6 Babeș-Bolyai UniversityRomania 21 works
  7. 7 Zhytomyr Ivan Franko State UniversityUkraine 21 works
  8. 8 Centre National de la Recherche ScientifiqueFrance 20 works
  9. 9 Technical University of Cluj-NapocaRomania 18 works
  10. 10 COMSATS University IslamabadPakistan 17 works

Who are the leading researchers in Analytic and geometric function theory?

The most-cited researchers publishing on Analytic and geometric function theory include John A. Todd and Dumitru Bǎleanu.

  1. 1 John A. Todd United Kingdom 107k citations
  2. 2 Dumitru Bǎleanu Türkiye 89k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Analytic and geometric function theory?

The most cited paper in Analytic and geometric function theory is "Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree" (Holger Wendland, 1995), with 3,058 citations. Next come "Quasiconformal maps in metric spaces with controlled geometry" (942) and "Subclasses of univalent functions" (851).

Most cited papers
#PaperReleasedCitations
1 Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree Holger Wendland · Advances in Computational Mathematics Dec 1995 3,058
2 Quasiconformal maps in metric spaces with controlled geometry Juha Heinonen, Pekka Koskela · Acta Mathematica Open access 1998 942
3 Subclasses of univalent functions Grigore Stefan Sǎlǎgean · Lecture notes in mathematics Book chapter 1983 851
4 The Lp-integrability of the partial derivatives of A quasiconformal mapping F. W. Gehring · Acta Mathematica Open access 1973 792
5 On the variation in the cohomology of the symplectic form of the reduced phase space J. J. Duistermaat, Gerrit Heckman · Inventiones mathematicae Jun 1982 791
All 100 most cited papers, with filters and sorting

Where is Analytic and geometric function theory research done?

The largest centres of Analytic and geometric function theory research in 2022-now are Moscow (Russia), Ad Dīwānīyah (Iraq), Cluj-Napoca (Romania) and Riyadh (Saudi Arabia). Among places with at least 20 works in it, it is an unusually large share of all research in Oradea, Ad Dīwānīyah and Zhytomyr.

Largest cities, 2022-now

  1. 1 MoscowRussia 52 works
  2. 2 Ad DīwānīyahIraq 51 works
  3. 3 Cluj-NapocaRomania 40 works
  4. 4 RiyadhSaudi Arabia 39 works
  5. 5 OradeaRomania 38 works
  6. 6 New DelhiIndia 29 works
  7. 7 BeijingChina 28 works
  8. 8 BaghdadIraq 26 works
  9. 9 ChennaiIndia 25 works
  10. 10 VelloreIndia 24 works

Where it is the local speciality

  1. OradeaRO · 38.1 works177×
  2. Ad DīwānīyahIQ · 51.5 works144×
  3. ZhytomyrUA · 21.3 works112×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Analytic and geometric function theory than the world average.

See Analytic and geometric function theory on the map

Where is the best place to study Analytic and geometric function theory?

Among universities, judged by research, University of Oradea, Technical University of Cluj-Napoca and University of Al-Qadisiyah score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%10%20%30%mean 20.03%fractional works in this field (log) →share of work in the world top 10% →University of OradeaTechnical University…Babeș-Bolyai Univers…University of Al-Qad…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1University of OradeaRomania 87.826.9%217.5×38 +132.9%
2Technical University of Cluj-NapocaRomania 71.123.5%63.4×18 +367.9%
3University of Al-QadisiyahIraq 67.710.7%164.1×52 +47.9%
4Babeș-Bolyai UniversityRomania 65.819.7%43.5×21 +7.1%
5Al al-Bayt UniversityJordan 64.123.6%104.1×9 +45.6%
6Vellore Institute of Technology UniversityIndia 62.615.6%12.0×24 +18.6%
7King Saud UniversitySaudi Arabia 60.522.2%6.7×13 +656.1%
8Al-Balqa Applied UniversityJordan 60.317.9%49.2×11 +296.6%
9Delhi Technological UniversityIndia 60.019.3%26.7×15 +350.7%
10Government College University, FaisalabadPakistan 57.020.9%28.0×9 -11.2%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Analytic and geometric function theory, country by country

Is Analytic and geometric function theory research growing?

Output in 2022-2025 was 9% higher than in 2018-2021, peaking in 2023. The fastest-growing topics are Analytic and geometric function theory.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Analytic and geometric function theory as a percentage of every work published that year, 0.0084% in 2024.

still counting0.010%0.020%0.030%Analytic and geometric function theory0.0086% in 202519801990200020102020

Fractional works of Analytic and geometric function theory over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Analytic and geometric function theory9.9% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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