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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. 10.1% 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%
1.7k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+14%
the tick is no change
Largest producer
China
24% of the 10 largest, 2022-now
Geometry and complex manifolds

Which countries lead Geometry and complex manifolds research?

By volume, China and the United States publish the most (562 and 482 works in 2022-now).

By volume, 2022-now

  1. 1 China 562 works
  2. 2 United States 482 works
  3. 3 France 223 works
  4. 4 India 196 works
  5. 5 Japan 175 works
  6. 6 Germany 161 works
  7. 7 Italy 156 works
  8. 8 Brazil 118 works
  9. 9 Türkiye 116 works
  10. 10 United Kingdom 109 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: 24.4%United States: 21.0%France: 9.7%India: 8.5%6 others listed: 36.3%24%largest
China562 · 24.4%United States482 · 21.0%France223 · 9.7%India196 · 8.5%6 others listed836 · 36.3%

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

Which institutions lead Geometry and complex manifolds research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Geometry and complex manifolds research, followed by Russian Academy of Sciences and Chinese Academy of Sciences.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 114 works
  2. 2 Russian Academy of SciencesRussia 33 works
  3. 3 Chinese Academy of SciencesChina 26 works
  4. 4 Peking UniversityChina 26 works
  5. 5 Tsinghua UniversityChina 26 works
  6. 6 Fudan UniversityChina 22 works
  7. 7 University of Science and Technology of ChinaChina 21 works
  8. 8 Massachusetts Institute of TechnologyUnited States 19 works
  9. 9 Max Planck SocietyGermany 15 works
  10. 10 University of OxfordUnited Kingdom 15 works

Who are the leading researchers in Geometry and complex manifolds?

The most-cited researchers publishing on Geometry and complex manifolds include Edward H. Witten and B. S. Acharya.

  1. 1 Edward H. Witten United States 174k citations
  2. 2 B. S. Acharya France 164k 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 Geometry and complex manifolds?

The most cited paper in Geometry and complex manifolds is "Análisis Comparativo y Refutación Determinista de la Incertidumbre Cuántica Óptica de Fluidos en la Variedad RP3 vs. Ortodoxia Probabilística" (Perelman, Grisha, 2002), with 2,563 citations. Next come "On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I" (2,475) and "Spectral asymmetry and Riemannian Geometry. I" (2,098).

Most cited papers
#PaperReleasedCitations
1 Análisis Comparativo y Refutación Determinista de la Incertidumbre Cuántica Óptica de Fluidos en la Variedad RP3 vs. Ortodoxia Probabilística Perelman, Grisha · arXiv (Cornell University) PreprintOpen access 11 Nov 2002 2,563
2 On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I Shing–Tung Yau · Communications on Pure and Applied Mathematics May 1978 2,475
3 Spectral asymmetry and Riemannian Geometry. I Michael Francis Atiyah, V. K. Patodi, I. M. Singer · Mathematical Proceedings of the Cambridge Philosophical Society 1975 2,098
4 Pseudo holomorphic curves in symplectic manifolds Mikhail Leonidovich Gromov · Inventiones mathematicae Jun 1985 2,092
5 The Yang-Mills equations over Riemann surfaces Michael Francis Atiyah, Raoul Bott · Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences 17 Mar 1983 2,033
All 98 most cited papers, with filters and sorting

Where is Geometry and complex manifolds research done?

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

Largest cities, 2022-now

  1. 1 BeijingChina 134 works
  2. 2 ParisFrance 81 works
  3. 3 ShanghaiChina 59 works
  4. 4 MoscowRussia 56 works
  5. 5 TokyoJapan 51 works
  6. 6 New YorkUnited States 35 works
  7. 7 SeoulSouth Korea 31 works
  8. 8 NanjingChina 29 works
  9. 9 MilanItaly 27 works
  10. 10 WuhanChina 26 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, Massachusetts Institute of Technology, New York University and University of Oxford 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 18.79%fractional works in this field (log) →share of work in the world top 10% →University of OxfordMassachusetts Instit…New York UniversityPeking University
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
1Massachusetts Institute of TechnologyUnited States 80.721.6%10.0×19 +15.6%
2New York UniversityUnited States 67.116.2%3.7×12 +116.6%
3University of OxfordUnited Kingdom 63.924.3%3.8×15 -13.5%
4Peking UniversityChina 62.611.0%4.7×26 +8.4%
5University of ViennaAustria 61.715.3%10.4×14 +40.3%
6Columbia UniversityUnited States 61.719.3%4.7×14 +11.6%
7University of TorontoCanada 60.626.7%2.3×13 +17.1%
8Imperial College LondonUnited Kingdom 59.523.3%3.3×9 +4.4%
9Tsinghua UniversityChina 57.711.2%4.1×26 -3.8%
10Imam Khomeini International UniversityIran 57.719.0%85.6×13 +116.7%

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 Geometry and complex manifolds, country by country

Is Geometry and complex manifolds research growing?

Output in 2022-2025 was 14% higher than in 2018-2021, peaking in 2022. The fastest-growing topics are Geometry and complex manifolds.

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 Geometry and complex manifolds as a percentage of every work published that year, 0.012% in 2024.

still counting0.010%0.020%0.030%Geometry and complex manifolds0.011% in 202519801990200020102020

Fractional works of Geometry and complex manifolds 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%Geometry and complex manifolds9.9% 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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