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Topic · Geometry and Topology

Geometry and complex manifolds

Geometry and complex manifolds is a research topic within Geometry and Topology. Science Explorer counts 17k research works in it since 1950. 18.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the geometry, stability, and properties of Kähler metrics, including topics such as scalar curvature, K-stability, complex Monge-Ampère equations, Ricci flow, Fano manifolds, Calabi-Yau manifolds, and geometric quantization.

  • Kähler Metrics
  • Stability
  • Scalar Curvature
  • K-Stability
  • Complex Monge-Ampère Equation
  • Ricci Flow
  • Fano Manifolds
  • Calabi-Yau Manifolds
  • Singularities
  • Geometric Quantization
Research works
17k
fractional, since 1950
In the world top 10%
3.1k
per year above
Top-10% rate
18.0%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+7%
the tick is no change

Which countries lead Geometry and complex manifolds research?

By volume, China and the United States publish the most (460 and 424 works in 2022–2025).

By volume, 2022–2025

  1. 1 China 460 works
  2. 2 United States 424 works
  3. 3 France 206 works
  4. 4 India 170 works
  5. 5 Japan 147 works
  6. 6 Germany 141 works
  7. 7 Italy 139 works
  8. 8 Türkiye 110 works
  9. 9 Brazil 109 works
  10. 10 United Kingdom 95 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.

China: 23.0%United States: 21.2%France: 10.3%India: 8.5%6 others listed: 37.0%23%largest
China460 · 23.0%United States424 · 21.2%France206 · 10.3%India170 · 8.5%6 others listed742 · 37.0%

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

Which institutions lead Geometry and complex manifolds research?

By volume in 2022–2025, Centre National de la Recherche Scientifique publishes the most Geometry and complex manifolds research, followed by Peking University and Tsinghua University.

By volume, 2022–2025

  1. 1 Centre National de la Recherche ScientifiqueFrance 35 works
  2. 2 Peking UniversityChina 21 works
  3. 3 Tsinghua UniversityChina 19 works
  4. 4 University of Science and Technology of ChinaChina 19 works
  5. 5 Fudan UniversityChina 18 works
  6. 6 Wuhan UniversityChina 13 works
  7. 7 Universidade Federal de Campina GrandeBrazil 13 works
  8. 8 Imam Khomeini International UniversityIran 13 works
  9. 9 Columbia UniversityUnited States 13 works
  10. 10 University of ViennaAustria 13 works

Who are the leading researchers in Geometry and complex manifolds?

The most-cited researchers publishing on Geometry and complex manifolds include Shing–Tung Yau, S. Ferrara and Luis Caffarelli.

  1. 1 Shing–Tung Yau United States 2.1k citations
  2. 2 S. Ferrara Switzerland 1.9k citations
  3. 3 Luis Caffarelli United States 1.5k citations

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

Where is Geometry and complex manifolds research done?

The largest centres of Geometry and complex manifolds research in 2022–2025 are Beijing (China), Paris (France), Shanghai (China) and Moscow (Russia).

Largest cities, 2022–2025

  1. 1 Beijing China 113 works
  2. 2 Paris France 75 works
  3. 3 Shanghai China 49 works
  4. 4 Moscow Russia 48 works
  5. 5 Tokyo Japan 42 works
  6. 6 New York United States 32 works
  7. 7 Seoul South Korea 27 works
  8. 8 Nanjing China 26 works
  9. 9 Milan Italy 25 works
  10. 10 Wuhan China 23 works
See Geometry and complex manifolds on the map

Where is the best place to study Geometry and complex manifolds?

Among universities, judged by research, Imam Khomeini International University, Massachusetts Institute of Technology and University of Vienna 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%20%40%mean 25.94%fractional works in this node (log) →share in the world top 10% →Imam Khomeini International University: 13, 21.6%Massachusetts Institute of Technology: 12, 34.4%University of Vienna: 13, 20.8%Jazan University: 9, 23.3%University of Warwick: 10, 27.5%Northwestern University: 8, 42.8%Kyungpook National University: 11, 20.4%Sorbonne Université: 12, 21.8%University of Bonn: 9, 25.1%Université Paris-Saclay: 9, 21.7%Massachusetts Instit…Jazan UniversityImam Khomeini Intern…University of Vienna
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Imam Khomeini International UniversityIran 60.521.6%85.2×13 +166.7%
2 Massachusetts Institute of TechnologyUnited States 57.634.4%7.2×12 +72.6%
3 University of ViennaAustria 56.720.8%9.8×13 +65.8%
4 Jazan UniversitySaudi Arabia 55.023.3%15.9×9 —
5 University of WarwickUnited Kingdom 54.427.5%8.3×10 +77.3%
6 Northwestern UniversityUnited States 53.242.8%4.5×8 +148.8%
7 Kyungpook National UniversitySouth Korea 50.720.4%12.1×11 +43.8%
8 Sorbonne UniversitéFrance 50.421.8%8.8×12 +1.8%
9 University of BonnGermany 48.425.1%9.8×9 -24.2%
10 Université Paris-SaclayFrance 48.221.7%8.4×9 —

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Geometry and complex manifolds research growing?

Output in 2018–2022 was 7% higher than in 2013–2017, peaking in 2022. The fastest-growing topics are Geometry and complex manifolds.

19801990200020102020
grewheldshrank

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

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.