Geometric Analysis and Curvature Flows
Geometric Analysis and Curvature Flows is a research topic within Applied Mathematics. Science Explorer counts 26k research works in it since 1950. 16.2% of them reached the world's top 10% most cited for their field and year.
This cluster of papers explores the mathematical theory and applications of optimal transport, including topics such as Ricci curvature, Wasserstein distance, metric measure spaces, gradient flows, Sobolev inequalities, the Monge-Kantorovich problem, mean curvature flow, and minimal surfaces.
- Optimal Transport
- Ricci Curvature
- Wasserstein Distance
- Metric Measure Spaces
- Gradient Flows
- Sobolev Inequalities
- Monge-Kantorovich Problem
- Mean Curvature Flow
- Geometric Applications
- Minimal Surfaces
- Research works
- 26k fractional, since 1950
- In the world top 10%
- 4.3k per year above
- Top-10% rate
- 16.2% share of its works in the world top 10%
- Growth, 2013–17 → 2018–22
- +10% the tick is no change
Which countries lead Geometric Analysis and Curvature Flows research?
By volume, China and the United States publish the most (842 and 616 works in 2022–2025).
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.
Shares of the rows listed above, not of the whole node.
Which institutions lead Geometric Analysis and Curvature Flows research?
By volume in 2022–2025, Centre National de la Recherche Scientifique publishes the most Geometric Analysis and Curvature Flows research, followed by Tsinghua University and University of Science and Technology of China.
By volume, 2022–2025
- 1 Centre National de la Recherche ScientifiqueFrance 38 works
- 2 Tsinghua UniversityChina 30 works
- 3 University of Science and Technology of ChinaChina 27 works
- 4 Universidad de GranadaSpain 27 works
- 5 Peking UniversityChina 24 works
- 6 Fudan UniversityChina 22 works
- 7 University of ViennaAustria 22 works
- 8 Wuhan UniversityChina 21 works
- 9 Imam Khomeini International UniversityIran 20 works
- 10 Universidade Federal de Campina GrandeBrazil 19 works
Who are the leading researchers in Geometric Analysis and Curvature Flows?
The most-cited researchers publishing on Geometric Analysis and Curvature Flows include Stanley Osher, Terence Tao and Élliott H. Lieb.
- 1 Stanley Osher United States 8k citations
- 2 Terence Tao United States 3.1k citations
- 3 Élliott H. Lieb United States 2.5k citations
- 4 G. W. Gibbons United Kingdom 2.2k citations
Ranked by citations received across their whole record, among researchers with at least three works on this topic.
Where is Geometric Analysis and Curvature Flows research done?
The largest centres of Geometric Analysis and Curvature Flows research in 2022–2025 are Beijing (China), Paris (France), Shanghai (China) and Moscow (Russia). Among places with at least 20 works in it, it is an unusually large share of all research in Qazvin.
Largest cities, 2022–2025
Where it is the local speciality
- QazvinIR · 20.3 works36×
Location quotient: how much more of its research is in Geometric Analysis and Curvature Flows than the world average.
Where is the best place to study Geometric Analysis and Curvature Flows?
Among universities, judged by research, Hangzhou Normal University, Imam Khomeini International University and University of Jyväskylä 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.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | Hangzhou Normal UniversityChina | 63.9 | 57.5% | 12.3× | 11 | +4.2% |
| 2 | Imam Khomeini International UniversityIran | 63.1 | 17.3% | 82.7× | 20 | +466.7% |
| 3 | University of JyväskyläFinland | 61.6 | 32.9% | 20.2× | 16 | +57.1% |
| 4 | Jazan UniversitySaudi Arabia | 60.7 | 18.9% | 12.9× | 12 | +345.9% |
| 5 | University of ViennaAustria | 60.1 | 20.7% | 10.3× | 22 | +64.8% |
| 6 | Imam Mohammad ibn Saud Islamic UniversitySaudi Arabia | 58.1 | 22.8% | 17.2× | 14 | — |
| 7 | Stony Brook UniversityUnited States | 53.6 | 26.7% | 10.7× | 14 | +39.5% |
| 8 | Courant Institute of Mathematical SciencesUnited States | 53.3 | 32.8% | 101.8× | 10 | +10.6% |
| 9 | Université Mustapha Stambouli de MascaraAlgeria | 51.8 | 7.6% | 83.0× | 11 | +242.5% |
| 10 | Universidad de GranadaSpain | 50.9 | 11.3% | 11.8× | 27 | -30.6% |
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 Geometric Analysis and Curvature Flows research growing?
Output in 2018–2022 was 10% higher than in 2013–2017, peaking in 2023. The fastest-growing topics are Geometric Analysis and Curvature Flows.
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.