Dan Knopf

2.0k total citations · 1 hit paper
26 papers, 1.0k citations indexed

About

Dan Knopf is a scholar working on Applied Mathematics, Geometry and Topology and Astronomy and Astrophysics. According to data from OpenAlex, Dan Knopf has authored 26 papers receiving a total of 1.0k indexed citations (citations by other indexed papers that have themselves been cited), including 26 papers in Applied Mathematics, 21 papers in Geometry and Topology and 18 papers in Astronomy and Astrophysics. Recurrent topics in Dan Knopf's work include Geometric Analysis and Curvature Flows (26 papers), Geometry and complex manifolds (20 papers) and Advanced Differential Geometry Research (15 papers). Dan Knopf is often cited by papers focused on Geometric Analysis and Curvature Flows (26 papers), Geometry and complex manifolds (20 papers) and Advanced Differential Geometry Research (15 papers). Dan Knopf collaborates with scholars based in United States, Taiwan and Canada. Dan Knopf's co-authors include Bennett Chow, Sigurd Angenent, James Isenberg, Tom Ilmanen, Christine Guenther, Mikhail Feldman, Lei Ni, Tom Ivey, David Glickenstein and Feng Luo and has published in prestigious journals such as Journal of Differential Geometry, Proceedings of the American Mathematical Society and Memoirs of the American Mathematical Society.

In The Last Decade

Dan Knopf

25 papers receiving 937 citations

Hit Papers

The Ricci Flow: An Introduction 2004 2026 2011 2018 2004 100 200 300
What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

  1. The Ricci Flow: An Introduction
    2004 336 citations Bennett Chow, Dan Knopf Mathematical surveys and monographs profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
Dan Knopf United States 13 969 865 585 82 72 26 1.0k
Lei Ni United States 23 1.6k 1.6× 1.3k 1.5× 699 1.2× 142 1.7× 46 0.6× 55 1.6k
Huai-Dong Cao United States 20 1.4k 1.5× 1.3k 1.5× 812 1.4× 113 1.4× 87 1.2× 53 1.5k
Peter M. Topping United Kingdom 17 687 0.7× 501 0.6× 259 0.4× 121 1.5× 33 0.5× 45 756
F. Tricerri Italy 13 749 0.8× 635 0.7× 510 0.9× 155 1.9× 36 0.5× 25 847
Paul Baird France 15 760 0.8× 617 0.7× 339 0.6× 109 1.3× 38 0.5× 48 831
Andrea Mondino United Kingdom 14 594 0.6× 327 0.4× 189 0.3× 94 1.1× 41 0.6× 50 643
Giovanni Calvaruso Italy 18 1.1k 1.2× 979 1.1× 907 1.6× 67 0.8× 37 0.5× 115 1.2k
Demir N. Küpeli Türkiye 11 415 0.4× 290 0.3× 332 0.6× 40 0.5× 57 0.8× 29 467
Cıhan Özgür Türkiye 17 711 0.7× 508 0.6× 502 0.9× 17 0.2× 31 0.4× 99 761
Oldřich Kowalski Czechia 19 1.2k 1.2× 983 1.1× 978 1.7× 201 2.5× 21 0.3× 106 1.4k

Countries citing papers authored by Dan Knopf

Since Specialization
Citations

This map shows the geographic impact of Dan Knopf's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Dan Knopf with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Dan Knopf more than expected).

Fields of papers citing papers by Dan Knopf

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Dan Knopf. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Dan Knopf. The network helps show where Dan Knopf may publish in the future.

Co-authorship network of co-authors of Dan Knopf

This figure shows the co-authorship network connecting the top 25 collaborators of Dan Knopf. A scholar is included among the top collaborators of Dan Knopf based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Dan Knopf. Dan Knopf is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Angenent, Sigurd & Dan Knopf. (2022). Ricci Solitons, Conical Singularities, and Nonuniqueness. Geometric and Functional Analysis. 32(3). 411–489. 9 indexed citations
2.
3.
Knopf, Dan & Nataša Šešum. (2018). Dynamic Instability of $$\mathbb {CP}^N$$ Under Ricci Flow. Journal of Geometric Analysis. 29(1). 902–916. 3 indexed citations
4.
Angenent, Sigurd, James Isenberg, & Dan Knopf. (2013). Degenerate neckpinches in Ricci flow. Journal für die reine und angewandte Mathematik (Crelles Journal). 2015(709). 81–117. 13 indexed citations
5.
Chow, Bennett, Sun-Chin Chu, David Glickenstein, et al.. (2010). Geometric-analytic aspects. American Mathematical Society eBooks. 3 indexed citations
6.
Knopf, Dan, et al.. (2010). Cross curvature flow on a negatively curved solid torus. Algebraic & Geometric Topology. 10(1). 343–372. 6 indexed citations
7.
Chow, Bennett, Sun-Chin Chu, David Glickenstein, et al.. (2010). The Ricci Flow: Techniques and Applications. Mathematical surveys and monographs. 48 indexed citations
8.
Knopf, Dan. (2009). Estimating the trace-free Ricci tensor in Ricci flow. Proceedings of the American Mathematical Society. 137(9). 3099–3103. 14 indexed citations
9.
Knopf, Dan. (2009). Convergence and Stability of Locally ℝ N -Invariant Solutions of Ricci Flow. Journal of Geometric Analysis. 19(4). 817–846. 7 indexed citations
10.
Knopf, Dan, et al.. (2008). Asymptotic stability of the cross curvature flow at a hyperbolic metric. Proceedings of the American Mathematical Society. 137(2). 699–709. 10 indexed citations
11.
Chow, Bennett, Sun-Chin Chu, David Glickenstein, et al.. (2007). The Ricci Flow: Techniques and Applications. Mathematical surveys and monographs. 87 indexed citations
12.
Chow, Bennett, Sun-Chin Chu, David Glickenstein, et al.. (2007). The Ricci Flow: Techniques and Applications. Mathematical surveys and monographs. 150 indexed citations
13.
Angenent, Sigurd & Dan Knopf. (2007). Precise asymptotics of the Ricci flow neckpinch. Communications in Analysis and Geometry. 15(4). 773–844. 26 indexed citations
14.
Chow, Bennett & Dan Knopf. (2004). The Ricci Flow: An Introduction. Mathematical surveys and monographs. 336 indexed citations breakdown →
15.
Angenent, Sigurd & Dan Knopf. (2004). An example of neckpinching for Ricci flow on $S^{n+1}$. Mathematical Research Letters. 11(4). 493–518. 47 indexed citations
16.
Feldman, Mikhail, Tom Ilmanen, & Dan Knopf. (2003). Rotationally Symmetric Shrinking and Expanding Gradient Kähler-Ricci Solitons. Journal of Differential Geometry. 65(2). 125 indexed citations
17.
Chow, Bennett & Dan Knopf. (2002). New Li-Yau-Hamilton Inequalities for the Ricci Flow via the Space-Time Approach. Journal of Differential Geometry. 60(1). 13 indexed citations
18.
Chow, Bennett, Dan Knopf, & Peng Lü. (2002). Hamilton’s injectivity radius estimate for sequences with almost nonnegative curvature operators. Communications in Analysis and Geometry. 10(5). 1151–1180. 2 indexed citations
19.
Knopf, Dan & Kevin McLeod. (2001). Quasi-convergence of model geometries under the Ricci flow. Communications in Analysis and Geometry. 9(4). 879–919. 24 indexed citations
20.
Knopf, Dan. (2000). Quasi-convergence of the Ricci flow. Communications in Analysis and Geometry. 8(2). 375–391. 12 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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