Bernd Kirchheim

1.8k total citations
34 papers, 904 citations indexed

About

Bernd Kirchheim is a scholar working on Applied Mathematics, Geometry and Topology and Computational Theory and Mathematics. According to data from OpenAlex, Bernd Kirchheim has authored 34 papers receiving a total of 904 indexed citations (citations by other indexed papers that have themselves been cited), including 21 papers in Applied Mathematics, 18 papers in Geometry and Topology and 13 papers in Computational Theory and Mathematics. Recurrent topics in Bernd Kirchheim's work include Nonlinear Partial Differential Equations (11 papers), Optimization and Variational Analysis (10 papers) and Analytic and geometric function theory (9 papers). Bernd Kirchheim is often cited by papers focused on Nonlinear Partial Differential Equations (11 papers), Optimization and Variational Analysis (10 papers) and Analytic and geometric function theory (9 papers). Bernd Kirchheim collaborates with scholars based in Germany, United Kingdom and Slovakia. Bernd Kirchheim's co-authors include Luigi Ambrosio, Jan Kristensen, J. M. Ball, Georg Dolzmann, Aldo Pratelli, Francesco Serra Cassano, Miroslav Chlebík, Sergio Conti, Tatiana Toro and Carlos E. Kenig and has published in prestigious journals such as Journal of Mathematical Analysis and Applications, Transactions of the American Mathematical Society and Archive for Rational Mechanics and Analysis.

In The Last Decade

Bernd Kirchheim

32 papers receiving 795 citations

Peers

Bernd Kirchheim

CTM

Guido De Philippis Italy

Ernst Kuwert Germany

Jussi Väısälä Finland

Rafael López Spain

Heinz Hopf Germany

V. M. Gol′dshteĭn Russia

Harold Rosenberg France

Vladimir Ryazanov Ukraine

Ulrich Dierkes Germany

Yoshihiro Tonegawa Japan

Guido De Philippis Italy

Bernd Kirchheim

622 ×0.9

203 ×0.5

215 ×0.7

299 ×1.1

CTM

31 ×0.3

Citations per year, relative to Bernd Kirchheim Bernd Kirchheim (= 1×) peers Guido De Philippis

Countries citing papers authored by Bernd Kirchheim

Since Specialization

Citations

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

Fields of papers citing papers by Bernd Kirchheim

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

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

Co-authorship network of co-authors of Bernd Kirchheim

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

All Works

Sort: Min cites: Since: Top N: Style:

20 of 20 papers shown

Kenig, Carlos E., Bernd Kirchheim, Jill Pipher, & Tatiana Toro. (2014). 4 Square Functions and the A ∞ Property of Elliptic Measures. 10 indexed citations

Kirchheim, Bernd & Jan Kristensen. (2011). Automatic convexity of rank-1 convex functions. Comptes Rendus Mathématique. 349(7-8). 407–409. 15 indexed citations

Kirchheim, Bernd, et al.. (2010). Monotone curves. Mathematische Annalen. 351(1). 81–94.

Kirchheim, Bernd & László Székelyhidi. (2008). On the gradient set of Lipschitz maps. Journal für die reine und angewandte Mathematik (Crelles Journal). 2008(625). 6 indexed citations

Csörnyei, Marianna, et al.. (2008). Universal Singular Sets in the Calculus of Variations. Archive for Rational Mechanics and Analysis. 190(3). 371–424. 6 indexed citations

Conti, Sergio, Georg Dolzmann, Bernd Kirchheim, & Stefan Müller. (2006). Sufficient conditions for the validity of the Cauchy-Born rule close to SO(n). Journal of the European Mathematical Society. 8(3). 515–539. 24 indexed citations

Ambrosio, Luigi, Bernd Kirchheim, & Aldo Pratelli. (2004). Existence of optimal transport maps for crystalline norms. Duke Mathematical Journal. 125(2). 39 indexed citations

Dolzmann, Georg & Bernd Kirchheim. (2003). Liquid-like behavior of shape memory alloys. Comptes Rendus Mathématique. 336(5). 441–446. 5 indexed citations

Chlebík, Miroslav & Bernd Kirchheim. (2002). Rigidity for the four gradient problem. Journal für die reine und angewandte Mathematik (Crelles Journal). 2002(551). 1–9. 22 indexed citations

10.

Kirchheim, Bernd & David Preiss. (2002). Uniformly Distributed Measures in Euclidean Spaces. MATHEMATICA SCANDINAVICA. 90(1). 152–152. 12 indexed citations

11.

Kirchheim, Bernd. (2001). Deformations with finitely many gradients and stability of quasiconvex hulls. Comptes Rendus de l Académie des Sciences - Series I - Mathematics. 332(3). 289–294. 26 indexed citations

12.

Dolzmann, Georg, Bernd Kirchheim, Stefan Müller, & Vladimír Šverák. (2000). The two-well problem in three dimensions. Calculus of Variations and Partial Differential Equations. 10(1). 21–40. 7 indexed citations

13.

Ball, J. M., Bernd Kirchheim, & Jan Kristensen. (2000). Regularity of quasiconvex envelopes. Calculus of Variations and Partial Differential Equations. 11(4). 333–359. 61 indexed citations

14.

Kirchheim, Bernd. (1998). Lipschitz minimizers of the 3-well problem having gradients of bounded variation. 12 indexed citations

15.

Kirchheim, Bernd. (1995). Hausdorff Measure and Level Sets of Typical Continuous Mappings in Euclidean Spaces. Transactions of the American Mathematical Society. 347(5). 1763–1763. 1 indexed citations

16.

Kirchheim, Bernd. (1995). Hausdorff measure and level sets of typical continuous mappings in Euclidean spaces. Transactions of the American Mathematical Society. 347(5). 1763–1777. 8 indexed citations

17.

Kirchheim, Bernd. (1994). Rectifiable Metric Spaces: Local Structure and Regularity of the Hausdorff Measure. Proceedings of the American Mathematical Society. 121(1). 113–113. 51 indexed citations

18.

Kirchheim, Bernd. (1994). Rectifiable metric spaces: local structure and regularity of the Hausdorff measure. Proceedings of the American Mathematical Society. 121(1). 113–123. 132 indexed citations

19.

Kirchheim, Bernd. (1990). A CHAOTIC FUNCTION WITH ZERO TOPOLOGICAL ENTROPY HAVING A NON-PERFECT ATTRACTOR. Mathematica Slovaca. 40(3). 267–272. 3 indexed citations

20.

Богачев, В. И., Bernd Kirchheim, & Walter Schachermayer. (1989). Continuous restrictions of linear maps between Banach spaces. Czech digital mathematics library. 30(2). 31–35. 2 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.

Explore authors with similar magnitude of impact