Topic · Geometry and complex manifolds
Most cited papers in Geometry and complex manifolds
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).
Showing 50 of 98 papers. Every paper with more than 425 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 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) | 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 |
| 6 | The Self-Duality Equations on a Riemann Surface Nigel James Hitchin · Proceedings of the London Mathematical Society | Jul 1987 | 1,788 |
| 7 | Polar factorization and monotone rearrangement of vector‐valued functions Yann Brenier · Communications on Pure and Applied Mathematics | Jun 1991 | 1,719 |
| 8 | A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem Jean‐David Benamou, Yann Brenier · Numerische Mathematik | 2000 | 1,694 |
| 9 | A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory Philip Candelas, Xenia C. de la Ossa, Paul S. Green et al. · Nuclear Physics B | Jul 1991 | 1,489 |
| 10 | Reduction of symplectic manifolds with symmetry Jerrold Eldon Marsden, Alan Weinstein · Reports on Mathematical Physics | Feb 1974 | 1,474 |
| 11 | Evidence for F-theory Cumrun Vafa · Nuclear Physics B | Jun 1996 | 1,340 |
| 12 | Ricci curvature for metric-measure spaces via optimal transport John A. Lott, Cédric Villani · Annals of Mathematics | 22 Apr 2009 | 1,304 |
| 13 | On the geometry of metric measure spaces. II Karl‐Theodor Sturm · Acta Mathematica | 2006 | 1,258 |
| 14 | Harmonic functions on complete riemannian manifolds Shing‐Tung Yau · Communications on Pure and Applied Mathematics | Mar 1975 | 1,249 |
| 15 | Random Fields and Geometry Robert J. Adler, Jonathan Taylor | 12 Jun 2007 | 1,122 |
| 16 | Real hypersurfaces in complex manifolds Shiing-Shen Chern, Jürgen Moser · Acta Mathematica | 1974 | 1,060 |
| 17 | Systematics of Moduli Stabilisation in Calabi-Yau Flux Compactifications Vijay Balasubramanian, Per Berglund, Joseph P Conlon et al. · Journal of High Energy Physics | 2 Mar 2005 | 1,028 |
| 18 | Superconformal field theory on threebranes at a Calabi-Yau singularity Igor R. Klebanov, Edward Witten · Nuclear Physics B | Dec 1998 | 1,015 |
| 19 | Hyperkähler metrics and supersymmetry Nigel James Hitchin, A. Karlhede, Ulf Lindström et al. · Communications in Mathematical Physics | Dec 1987 | 1,012 |
| 20 | The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories Darryl D. Holm, Jerrold Eldon Marsden, Tudor Stefan Ratiu · Advances in Mathematics | Jul 1998 | 1,003 |
| 21 | Permutationally invariant potential energy surfaces in high dimensionality Bastiaan J. Braams, Joel M. Bowman · International Reviews in Physical Chemistry | Oct 2009 | 992 |
| 22 | Topological quantum field theory Michael Francis Atiyah · Publications mathématiques de l IHÉS | 7 Jan 1988 | 991 |
| 23 | CFT's from Calabi–Yau four-folds Sergei Gukov, Cumrun Vafa, Edward Witten · Nuclear Physics B | Sep 2000 | 990 |
| 24 | Asymptotic behavior for singularities of the mean curvature flow Gerhard Huisken · Journal of Differential Geometry | 1990 | 989 |
| 25 | Compactifications of F-theory on Calabi-Yau threefolds (II) David R. Morrison, Cumrun Vafa · Nuclear Physics B | Sep 1996 | 969 |
| 26 | A new capacity for plurisubharmonic functions Eric Bedford, B. A. Taylor · Acta Mathematica | 1982 | 964 |
| 27 | Strong coupling expansion of Calabi-Yau compactification Edward Witten · Nuclear Physics B | Jul 1996 | 953 |
| 28 | On the existence of hermitian-yang-mills connections in stable vector bundles Karen Uhlenbeck, Shing–Tung Yau · Communications on Pure and Applied Mathematics | 1986 | 952 |
| 29 | On the structure of spaces with Ricci curvature bounded below. I Jeff Cheeger, Tobias Colding · Journal of Differential Geometry | 1997 | 928 |
| 30 | The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian Luis A. Caffarelli, Louis Nirenberg, Joel Spruck · Acta Mathematica | 1985 | 898 |
| 31 | Variation of hodge structure: The singularities of the period mapping Wilfried Schmid · Inventiones mathematicae | Sep 1973 | 887 |
| 32 | Kähler-Einstein metrics with positive scalar curvature Gang Tian · Inventiones mathematicae | 3 Sep 1997 | 880 |
| 33 | Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds Alexander Asaturovich Grigor'yan · Bulletin of the American Mathematical Society | 19 Feb 1999 | 877 |
| 34 | Calabi's conjecture and some new results in algebraic geometry Shing–Tung Yau · Proceedings of the National Academy of Sciences | May 1977 | 805 |
| 35 | The sixteen classes of almost Hermitian manifolds and their linear invariants Alfred Gray, Luis Hervella · Annali di Matematica Pura ed Applicata (1923 -) | Dec 1980 | 800 |
| 36 | Real homotopy theory of K�hler manifolds Pierre Deligne, Phillip Griffiths, John S. Morgan et al. · Inventiones mathematicae | Oct 1975 | 797 |
| 37 | Complexity and shock wave geometries Douglas Stanford, Leonard Susskind · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields | 11 Dec 2014 | 782 |
| 38 | Positive scalar curvature and the Dirac operator on complete riemannian manifolds Mikhael Gromov, H. Blaine Lawson · Publications mathématiques de l IHÉS | 7 Dec 1983 | 757 |
| 39 | Comments on conifolds Philip Candelas, Xenia C. de la Ossa · Nuclear Physics B | Sep 1990 | 709 |
| 40 | The structure of complete stable minimal surfaces in 3‐manifolds of non‐negative scalar curvature D. Fischer-Colbrie, Richard Schoen · Communications on Pure and Applied Mathematics | Mar 1980 | 709 |
| 41 | A class of almost contact Riemannian manifolds Katsuei Kenmotsu · Tohoku Mathematical Journal | 1972 | 706 |
| 42 | The dirichlet problem for a complex Monge-Amp�re equation Eric Bedford, B. A. Taylor · Inventiones mathematicae | Feb 1976 | 699 |
| 43 | Nonlinear models in 2 + ε dimensions Daniel Friedan · Annals of Physics | Sep 1985 | 694 |
| 44 | Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group Benoı̂t Collins, Piotr Śniady · Communications in Mathematical Physics | 22 Mar 2006 | 676 |
| 45 | Generalized Complex Geometry Mario García-Fernández, Jeffrey D. Streets · University lecture series | 6 Apr 2021 | 651 |
| 46 | Type IIB Green–Schwarz superstring in plane wave Ramond–Ramond background R.R. Metsaev · Nuclear Physics B | Mar 2002 | 640 |
| 47 | Symplectic invariants and Hamiltonian dynamics Helmut Hofer, Eduard Zehnder · Birkhäuser Basel eBooks | 1995 | 636 |
| 48 | Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products Jeff Cheeger, Tobias Colding · Annals of Mathematics | Jul 1996 | 620 |
| 49 | Polynomial invariants for smooth four-manifolds Simon K Donaldson · Topology | 1990 | 620 |
| 50 | Operators with dense, invariant, cyclic vector manifolds Gilles Godefroy, Joel H. Shapiro · Journal of Functional Analysis | Jun 1991 | 605 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.