Harold Levine

1.3k total citations
19 papers, 507 citations indexed

About

Harold Levine is a scholar working on Geometry and Topology, Mathematical Physics and Computational Theory and Mathematics. According to data from OpenAlex, Harold Levine has authored 19 papers receiving a total of 507 indexed citations (citations by other indexed papers that have themselves been cited), including 7 papers in Geometry and Topology, 4 papers in Mathematical Physics and 4 papers in Computational Theory and Mathematics. Recurrent topics in Harold Levine's work include Mathematical Dynamics and Fractals (4 papers), Algebraic Geometry and Number Theory (3 papers) and Advanced Differential Equations and Dynamical Systems (3 papers). Harold Levine is often cited by papers focused on Mathematical Dynamics and Fractals (4 papers), Algebraic Geometry and Number Theory (3 papers) and Advanced Differential Equations and Dynamical Systems (3 papers). Harold Levine collaborates with scholars based in United States and Germany. Harold Levine's co-authors include A. O. Petters, J. Wambsganß, Bernard Teissier, David Eisenbud, Robert J. Fiel, Fred W. Billmeyer, E.H. Mark and Michael Shub and has published in prestigious journals such as Journal of Colloid and Interface Science, Archives of Biochemistry and Biophysics and Annals of Mathematics.

In The Last Decade

Harold Levine

18 papers receiving 428 citations

Peers

Harold Levine

NHEP

R. W. Sharpe Canada

H. E. Rauch United States

W. M. M�ller Germany

David Bleecker United States

Ernst Binz Germany

Edwin Ihrig United States

Boris N. Apanasov United States

Shun-ichi Tachibana Japan

Franklin P. Peterson United States

Bertfried Fauser Germany

R. W. Sharpe Canada

Harold Levine

162 ×0.8

81 ×0.5

137 ×1.0

107 ×1.2

45 ×0.7

NHEP

Citations per year, relative to Harold Levine Harold Levine (= 1×) peers R. W. Sharpe

Countries citing papers authored by Harold Levine

Since Specialization

Citations

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

Fields of papers citing papers by Harold Levine

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Harold Levine. 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 Harold Levine. The network helps show where Harold Levine may publish in the future.

Co-authorship network of co-authors of Harold Levine

This figure shows the co-authorship network connecting the top 25 collaborators of Harold Levine. A scholar is included among the top collaborators of Harold Levine 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 Harold Levine. Harold Levine is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

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19 of 19 papers shown

Petters, A. O., Harold Levine, & J. Wambsganß. (2001). Singularity Theory and Gravitational Lensing. Birkhäuser Boston eBooks. 179 indexed citations

Levine, Harold. (1995). Computing the Euler characteristic of a manifold with boundary. Proceedings of the American Mathematical Society. 123(8). 2563–2567. 1 indexed citations

Levine, Harold, A. O. Petters, & J. Wambsganß. (1993). Applications of singularity theory to gravitational lensing. I. Multiple lens planes. Journal of Mathematical Physics. 34(10). 4781–4808. 13 indexed citations

Levine, Harold. (1988). Stable mappings of 3-manifolds into the plane. Banach Center Publications. 20(1). 279–289. 1 indexed citations

Levine, Harold. (1985). Classifying Immersions into ℝ4 over Stable Maps of 3-Manifolds into ℝ2. Lecture notes in mathematics. 22 indexed citations

Levine, Harold, E.H. Mark, & Robert J. Fiel. (1978). Small-angle light scattering characteristics of pyran copolymer-divalent cation coacervates. Journal of Colloid and Interface Science. 63(2). 242–250. 1 indexed citations

Levine, Harold, E.H. Mark, & Robert J. Fiel. (1977). Divalent cation binding specificities and microsphere formation of pyran copolymer and related polycarboxylates. Archives of Biochemistry and Biophysics. 184(1). 156–165. 8 indexed citations

Eisenbud, David, Harold Levine, & Bernard Teissier. (1977). An Algebraic Formula for the Degree of a C ∞ Map Germ. Annals of Mathematics. 106(1). 19–19. 120 indexed citations

Levine, Harold. (1976). Stable maps: An introduction with low dimensional examples. Bulletin of the Brazilian Mathematical Society New Series. 7(2). 145–184. 13 indexed citations

10.

Levine, Harold, Robert J. Fiel, & Fred W. Billmeyer. (1976). Very low‐angle light scattering. A characterization method for high‐molecular‐weight DNA. Biopolymers. 15(7). 1267–1281. 6 indexed citations

11.

Fiel, Robert J., E.H. Mark, & Harold Levine. (1976). Polyanion induced nuclear swelling and microsphere formation. Journal of Colloid and Interface Science. 55(1). 133–142. 6 indexed citations

12.

Levine, Harold & Michael Shub. (1973). Stability of foliations. Transactions of the American Mathematical Society. 184(0). 419–437. 4 indexed citations

13.

Billmeyer, Fred W., et al.. (1971). The refraction correction in light scattering. Journal of Colloid and Interface Science. 35(2). 204–214. 9 indexed citations

14.

Levine, Harold. (1966). Mappings of Manifolds into the Plane. American Journal of Mathematics. 88(2). 357–357. 20 indexed citations

15.

Levine, Harold. (1965). Elimination of cusps. Topology. 3. 263–296. 52 indexed citations

16.

Levine, Harold. (1964). The singularities $S_{1}^{q}$. Illinois Journal of Mathematics. 8(1). 16 indexed citations

17.

Levine, Harold. (1963). Homotopic curves on surfaces. Proceedings of the American Mathematical Society. 14(6). 986–990. 13 indexed citations

18.

Levine, Harold. (1963). Homotopic Curves on Surfaces. Proceedings of the American Mathematical Society. 14(6). 986–986. 2 indexed citations

19.

Levine, Harold. (1960). A Theorem on Holomorphic Mappings into Complex Projective Space. Annals of Mathematics. 71(3). 529–529. 21 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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