Christopher B. Croke

2.5k total citations
57 papers, 1.4k citations indexed

About

Christopher B. Croke is a scholar working on Applied Mathematics, Geometry and Topology and Mathematical Physics. According to data from OpenAlex, Christopher B. Croke has authored 57 papers receiving a total of 1.4k indexed citations (citations by other indexed papers that have themselves been cited), including 40 papers in Applied Mathematics, 35 papers in Geometry and Topology and 14 papers in Mathematical Physics. Recurrent topics in Christopher B. Croke's work include Geometric Analysis and Curvature Flows (37 papers), Geometric and Algebraic Topology (20 papers) and Geometry and complex manifolds (12 papers). Christopher B. Croke is often cited by papers focused on Geometric Analysis and Curvature Flows (37 papers), Geometric and Algebraic Topology (20 papers) and Geometry and complex manifolds (12 papers). Christopher B. Croke collaborates with scholars based in United States, Russia and Israel. Christopher B. Croke's co-authors include Bruce Kleiner, Miloš Žefran, V. Kumar, V. A. Sharafutdinov, Mikhail G. Katz, Albert Fathi, N. S. Dairbekov, Hermann Karcher, Vijay Kumar and Viktor Schroeder and has published in prestigious journals such as The International Journal of Robotics Research, Journal of the Optical Society of America A and IEEE Transactions on Robotics and Automation.

In The Last Decade

Christopher B. Croke

55 papers receiving 1.2k citations

Peers — A (Enhanced Table)

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

Name h Career Trend Papers Cites
Christopher B. Croke United States 20 774 737 514 204 186 57 1.4k
Manfredo do Carmo Brazil 17 1.3k 1.7× 1.1k 1.4× 230 0.4× 273 1.3× 449 2.4× 46 2.0k
Ennio De Giorgi Italy 15 1.2k 1.6× 390 0.5× 590 1.1× 921 4.5× 98 0.5× 32 1.9k
Yuri L. Sachkov Russia 9 385 0.5× 304 0.4× 158 0.3× 107 0.5× 204 1.1× 21 988
Michael E. Gage United States 8 869 1.1× 466 0.6× 182 0.4× 193 0.9× 149 0.8× 17 1.3k
Eugenio Calabi United States 20 1.5k 1.9× 1.4k 1.9× 413 0.8× 176 0.9× 389 2.1× 31 2.1k
Peter Petersen United States 16 1.4k 1.8× 1.1k 1.5× 289 0.6× 119 0.6× 669 3.6× 56 1.6k
Yu. G. Reshetnyak Russia 21 1.2k 1.5× 843 1.1× 322 0.6× 494 2.4× 27 0.1× 70 1.6k
Ronald Gariepy United States 16 1.1k 1.4× 245 0.3× 482 0.9× 812 4.0× 29 0.2× 28 1.7k
Serge Tabachnikov United States 21 286 0.4× 908 1.2× 746 1.5× 159 0.8× 114 0.6× 129 1.5k
F. Silva Leite Portugal 17 231 0.3× 263 0.4× 90 0.2× 125 0.6× 150 0.8× 74 936

Countries citing papers authored by Christopher B. Croke

Since Specialization
Citations

This map shows the geographic impact of Christopher B. Croke'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 Christopher B. Croke with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Christopher B. Croke more than expected).

Fields of papers citing papers by Christopher B. Croke

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Christopher B. Croke. 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 Christopher B. Croke. The network helps show where Christopher B. Croke may publish in the future.

Co-authorship network of co-authors of Christopher B. Croke

This figure shows the co-authorship network connecting the top 25 collaborators of Christopher B. Croke. A scholar is included among the top collaborators of Christopher B. Croke 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 Christopher B. Croke. Christopher B. Croke 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.
Hicks, R. Andrew & Christopher B. Croke. (2010). Designing coupled free-form surfaces. Journal of the Optical Society of America A. 27(10). 2132–2132. 15 indexed citations
2.
Croke, Christopher B.. (2007). Small volume on big 𝑛-spheres. Proceedings of the American Mathematical Society. 136(2). 715–717. 2 indexed citations
3.
Croke, Christopher B.. (2005). Boundary and lens rigidity of finite quotients. Proceedings of the American Mathematical Society. 133(12). 3663–3668. 9 indexed citations
4.
Croke, Christopher B., Michael Vogelius, Günther Uhlmann, & Irena Lasiecka. (2004). Geometric Methods in Inverse Problems and PDE Control. CERN Document Server (European Organization for Nuclear Research). 33 indexed citations
5.
Ananthasuresh, G. K., et al.. (2004). Design of Reduced Protein Models by Energy Minimization Using Mathematical Programming. 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. 3 indexed citations
6.
Croke, Christopher B. & Bruce Kleiner. (2002). The geodesic flow of a nonpositively curved graph manifold. Geometric and Functional Analysis. 12(3). 479–545. 21 indexed citations
7.
Croke, Christopher B. & Bruce Kleiner. (2000). Spaces with nonpositive curvature and their ideal boundaries. Topology. 39(3). 549–556. 62 indexed citations
8.
Žefran, Miloš, Vijay Kumar, & Christopher B. Croke. (1999). Metrics and Connections for Rigid-Body Kinematics. The International Journal of Robotics Research. 18(2). 242–1. 38 indexed citations
9.
Croke, Christopher B. & Bruce Kleiner. (1998). A rigidity theorem for manifolds without conjugate points. Ergodic Theory and Dynamical Systems. 18(4). 813–829. 1 indexed citations
10.
Croke, Christopher B. & Bruce Kleiner. (1994). Conjugacy and rigidity for manifolds with a parallel vector field. Journal of Differential Geometry. 39(3). 32 indexed citations
11.
Croke, Christopher B., Albert Fathi, & Jacob J. Feldman. (1992). The marked length-spectrum of a surface of nonpositive curvature. Topology. 31(4). 847–855. 31 indexed citations
12.
Croke, Christopher B.. (1991). Simply connected manifolds with no conjugate points which are flat outside a compact set. Proceedings of the American Mathematical Society. 111(1). 297–298. 4 indexed citations
13.
Croke, Christopher B.. (1991). Simply Connected Manifolds with no Conjugate Points Which are Flat Outside a Compact Set. Proceedings of the American Mathematical Society. 111(1). 297–297. 1 indexed citations
14.
Croke, Christopher B.. (1991). Rigidity and the distance between boundary points. Journal of Differential Geometry. 33(2). 84 indexed citations
15.
Croke, Christopher B. & Hermann Karcher. (1988). Volumes of Small Balls on Open Manifolds: Lower Bounds and Examples. Transactions of the American Mathematical Society. 309(2). 753–753. 3 indexed citations
16.
Croke, Christopher B.. (1984). Curvature free volume estimates. Inventiones mathematicae. 76(3). 515–521. 12 indexed citations
17.
Croke, Christopher B.. (1983). On the volume of metric balls. Proceedings of the American Mathematical Society. 88(4). 660–664. 5 indexed citations
18.
Croke, Christopher B.. (1981). The first eigenvalue of the Laplacian for plane domains. Proceedings of the American Mathematical Society. 81(2). 304–305. 9 indexed citations
19.
Croke, Christopher B.. (1981). A “maximal torus” type theorem for complete Riemannian manifolds. Pacific Journal of Mathematics. 97(1). 65–73. 21 indexed citations
20.
Croke, Christopher B.. (1980). Riemannian manifolds with large invariants. Journal of Differential Geometry. 15(4). 4 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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