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Author ID: bar.christian Recent zbMATH articles by "Bär, Christian"
Published as: Bär, Christian; Bär, C.; Bär, Ch.
External Links: MGP · Wikidata · GND
Documents Indexed: 73 Publications since 1990, including 9 Books
4 Contributions as Editor
Reviewing Activity: 178 Reviews
Co-Authors: 29 Co-Authors with 37 Joint Publications
789 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

55 Publications have been cited 862 times in 620 Documents Cited by Year
Real Killing spinors and holonomy. Zbl 0778.53037
Bär, Christian
129
1993
Wave equations on Lorentzian manifolds and quantization. Zbl 1118.58016
Bär, Christian; Ginoux, Nicolas; Pfäffle, Frank
100
2007
Extrinsic bounds for eigenvalues of the Dirac operator. Zbl 0921.58065
Bär, Christian
69
1998
Generalized cylinders in semi-Riemannian and spin geometry. Zbl 1068.53030
Bär, Christian; Gauduchon, Paul; Moroianu, Andrei
60
2005
Metrics with harmonic spinors. Zbl 0867.53037
Bär, C.
40
1996
Zero sets of solutions to semilinear elliptic systems of first order. Zbl 0942.35064
Bär, Christian
40
1999
The Dirac operator on space forms of positive curvature. Zbl 0848.58046
Bär, Christian
35
1996
Lower eigenvalue estimates for Dirac operators. Zbl 0741.58046
Bär, Christian
33
1992
Green-hyperbolic operators on globally hyperbolic spacetimes. Zbl 1316.58027
Bär, Christian
31
2015
On Nodal Sets for Dirac and Laplace Operators. Zbl 0888.47028
Bär, Christian
26
1997
The Dirac operator on nilmanifolds and collapsing circle bundles. Zbl 0911.58037
Ammann, Bernd; Bär, Christian
24
1998
Classical and quantum fields on Lorentzian manifolds. Zbl 1254.81044
Bär, Christian; Ginoux, Nicolas
21
2012
Boundary value problems for elliptic differential operators of first order. Zbl 1331.58022
Bär, Christian; Ballmann, Werner
21
2012
Quantum field theory on curved spacetimes. Concepts and mathematical foundations. Extended lecture notes of the compact course quantum field theory on curved spacetimes, Potsdam, Germany, October 2007. Zbl 1178.81003
20
2009
The Dirac operator on hyperbolic manifolds of finite volume. Zbl 1030.58021
Bär, Christian
18
2000
Harmonic spinors on Riemann surfaces. Zbl 0763.30017
Bär, Christian; Schmutz, Paul
18
1992
The Dirac operator on homogeneous spaces and its spectrum on 3- dimensional lens spaces. Zbl 0786.53030
Bär, Christian
18
1992
Surgery and the spectrum of the Dirac operator. Zbl 1017.58019
Bär, Christian; Dahl, Mattias
13
2002
A rigorous geometric derivation of the chiral anomaly in curved backgrounds. Zbl 1350.81029
Bär, Christian; Strohmaier, Alexander
9
2016
Guide to elliptic boundary value problems for Dirac-type operators. Zbl 1377.58022
Bär, Christian; Ballmann, Werner
9
2016
An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary. Zbl 1429.83004
Bär, Christian; Strohmaier, Alexander
9
2019
Dirac eigenvalue estimates on surfaces. Zbl 1007.58014
Ammann, Bernd; Bär, Christian
8
2002
Initial value problems for wave equations on manifolds. Zbl 1338.58018
Bär, Christian; Wafo, Roger Tagne
8
2015
Stochastic completeness and volume growth. Zbl 1201.58024
Bär, Christian; Bessa, G. Pacelli
6
2010
CCR- versus CAR-quantization on curved spacetimes. Zbl 1250.81073
Bär, Christian; Ginoux, Nicolas
6
2012
Differential characters. Zbl 1296.58002
Bär, Christian; Becker, Christian
6
2014
Spectral bounds for Dirac operators on open manifolds. Zbl 1193.53119
Bär, Christian
6
2009
Harmonic spinors for twisted Dirac operators. Zbl 0889.53025
Bär, Christian
5
1997
The spectrum of Dirac operators. (Das Spektrum von Dirac-Operatoren.) Zbl 0748.53022
Bär, Christian
5
1990
Geometrically formal 4-manifolds with nonnegative sectional curvature. Zbl 1319.53027
Bär, Christian
5
2015
Asymptotic heat kernel expansion in the semi-classical limit. Zbl 1211.58018
Bär, Christian; Pfäffle, Frank
5
2010
The first Dirac eigenvalues on manifolds with positive scalar curvature. Zbl 1053.58012
Bär, Christian; Dahl, Mattias
5
2004
The Einstein-Hilbert action as a spectral action. Zbl 1255.81218
Ammann, Bernd; Bär, Christian
5
2002
Elementary differential geometry. 2nd revised and enlarged ed. (Elementare Differentialgeometrie.) Zbl 1191.53001
Bär, Christian
4
2010
Small eigenvalues of the conformal Laplacian. Zbl 1030.58003
Bär, Christian; Dahl, Matthias
4
2003
Path integrals on manifolds by finite dimensional approximation. Zbl 1165.58015
Bär, Christian; Pfäffle, Frank
4
2008
On harmonic spinors. Zbl 1010.58016
Bär, C.
4
1998
Differential characters and geometric chains. Zbl 1304.53019
Bär, Christian; Becker, Christian
3
2014
Semi-bounded restrictions of Dirac type operators and the unique continuation property. Zbl 1031.58008
Bär, Christian; Strohmaier, Alexander
3
2001
Heat kernel asymptotics for roots of generalized Laplacians. Zbl 1079.58020
Bär, Christian; Moroianu, Sergiu
3
2003
Wiener measures on Riemannian manifolds and the Feynman-Kac formula. Zbl 1302.58017
Bär, Christian; Pfäffle, Frank
2
2011
\(C^*\)-algebras. Zbl 1185.46037
Bär, Christian; Becker, Christian
2
2009
Conformal structures in noncommutative geometry. Zbl 1153.58010
Bär, Christian
2
2007
Dirac eigenvalues and total scalar curvature. Zbl 0960.58014
Ammann, Bernd; Bär, Christian
2
2000
Localization and semibounded energy – a weak unique continuation theorem. Zbl 0969.58007
Bär, Christian
2
2000
The Dirac determinant of spherical space forms. Zbl 1049.58030
Bär, Christian; Schopka, Sven
2
2003
Elliptic symbols. Zbl 0946.58020
Bär, Christian
2
1999
Upper eigenvalue estimates for Dirac operators. Zbl 0770.53026
Bär, Christian
2
1992
Dependence of the Dirac spectrum on the spin structure. Zbl 0995.58020
Bär, Christian
2
2000
The spectrum of the Dirac operator. Zbl 1103.58015
Bär, Christian
1
2005
A remark on positively curved 4-manifolds. Zbl 0796.53039
Bär, Christian
1
1994
Heat operator and \(\zeta\)-function estimates for surfaces. Zbl 0917.58047
Bär, Christian
1
1998
Renormalized integrals and a path integral formula for the heat kernel on a manifold. Zbl 1317.58039
Bär, Christian
1
2012
The Dirac fundamental tone of the hyperbolic space. Zbl 0757.53020
Bär, Christian
1
1992
Manifolds with many Rarita-Schwinger fields. Zbl 1479.53061
Bär, Christian; Mazzeo, Rafe
1
2021
Manifolds with many Rarita-Schwinger fields. Zbl 1479.53061
Bär, Christian; Mazzeo, Rafe
1
2021
An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary. Zbl 1429.83004
Bär, Christian; Strohmaier, Alexander
9
2019
A rigorous geometric derivation of the chiral anomaly in curved backgrounds. Zbl 1350.81029
Bär, Christian; Strohmaier, Alexander
9
2016
Guide to elliptic boundary value problems for Dirac-type operators. Zbl 1377.58022
Bär, Christian; Ballmann, Werner
9
2016
Green-hyperbolic operators on globally hyperbolic spacetimes. Zbl 1316.58027
Bär, Christian
31
2015
Initial value problems for wave equations on manifolds. Zbl 1338.58018
Bär, Christian; Wafo, Roger Tagne
8
2015
Geometrically formal 4-manifolds with nonnegative sectional curvature. Zbl 1319.53027
Bär, Christian
5
2015
Differential characters. Zbl 1296.58002
Bär, Christian; Becker, Christian
6
2014
Differential characters and geometric chains. Zbl 1304.53019
Bär, Christian; Becker, Christian
3
2014
Classical and quantum fields on Lorentzian manifolds. Zbl 1254.81044
Bär, Christian; Ginoux, Nicolas
21
2012
Boundary value problems for elliptic differential operators of first order. Zbl 1331.58022
Bär, Christian; Ballmann, Werner
21
2012
CCR- versus CAR-quantization on curved spacetimes. Zbl 1250.81073
Bär, Christian; Ginoux, Nicolas
6
2012
Renormalized integrals and a path integral formula for the heat kernel on a manifold. Zbl 1317.58039
Bär, Christian
1
2012
Wiener measures on Riemannian manifolds and the Feynman-Kac formula. Zbl 1302.58017
Bär, Christian; Pfäffle, Frank
2
2011
Stochastic completeness and volume growth. Zbl 1201.58024
Bär, Christian; Bessa, G. Pacelli
6
2010
Asymptotic heat kernel expansion in the semi-classical limit. Zbl 1211.58018
Bär, Christian; Pfäffle, Frank
5
2010
Elementary differential geometry. 2nd revised and enlarged ed. (Elementare Differentialgeometrie.) Zbl 1191.53001
Bär, Christian
4
2010
Quantum field theory on curved spacetimes. Concepts and mathematical foundations. Extended lecture notes of the compact course quantum field theory on curved spacetimes, Potsdam, Germany, October 2007. Zbl 1178.81003
20
2009
Spectral bounds for Dirac operators on open manifolds. Zbl 1193.53119
Bär, Christian
6
2009
\(C^*\)-algebras. Zbl 1185.46037
Bär, Christian; Becker, Christian
2
2009
Path integrals on manifolds by finite dimensional approximation. Zbl 1165.58015
Bär, Christian; Pfäffle, Frank
4
2008
Wave equations on Lorentzian manifolds and quantization. Zbl 1118.58016
Bär, Christian; Ginoux, Nicolas; Pfäffle, Frank
100
2007
Conformal structures in noncommutative geometry. Zbl 1153.58010
Bär, Christian
2
2007
Generalized cylinders in semi-Riemannian and spin geometry. Zbl 1068.53030
Bär, Christian; Gauduchon, Paul; Moroianu, Andrei
60
2005
The spectrum of the Dirac operator. Zbl 1103.58015
Bär, Christian
1
2005
The first Dirac eigenvalues on manifolds with positive scalar curvature. Zbl 1053.58012
Bär, Christian; Dahl, Mattias
5
2004
Small eigenvalues of the conformal Laplacian. Zbl 1030.58003
Bär, Christian; Dahl, Matthias
4
2003
Heat kernel asymptotics for roots of generalized Laplacians. Zbl 1079.58020
Bär, Christian; Moroianu, Sergiu
3
2003
The Dirac determinant of spherical space forms. Zbl 1049.58030
Bär, Christian; Schopka, Sven
2
2003
Surgery and the spectrum of the Dirac operator. Zbl 1017.58019
Bär, Christian; Dahl, Mattias
13
2002
Dirac eigenvalue estimates on surfaces. Zbl 1007.58014
Ammann, Bernd; Bär, Christian
8
2002
The Einstein-Hilbert action as a spectral action. Zbl 1255.81218
Ammann, Bernd; Bär, Christian
5
2002
Semi-bounded restrictions of Dirac type operators and the unique continuation property. Zbl 1031.58008
Bär, Christian; Strohmaier, Alexander
3
2001
The Dirac operator on hyperbolic manifolds of finite volume. Zbl 1030.58021
Bär, Christian
18
2000
Dirac eigenvalues and total scalar curvature. Zbl 0960.58014
Ammann, Bernd; Bär, Christian
2
2000
Localization and semibounded energy – a weak unique continuation theorem. Zbl 0969.58007
Bär, Christian
2
2000
Dependence of the Dirac spectrum on the spin structure. Zbl 0995.58020
Bär, Christian
2
2000
Zero sets of solutions to semilinear elliptic systems of first order. Zbl 0942.35064
Bär, Christian
40
1999
Elliptic symbols. Zbl 0946.58020
Bär, Christian
2
1999
Extrinsic bounds for eigenvalues of the Dirac operator. Zbl 0921.58065
Bär, Christian
69
1998
The Dirac operator on nilmanifolds and collapsing circle bundles. Zbl 0911.58037
Ammann, Bernd; Bär, Christian
24
1998
On harmonic spinors. Zbl 1010.58016
Bär, C.
4
1998
Heat operator and \(\zeta\)-function estimates for surfaces. Zbl 0917.58047
Bär, Christian
1
1998
On Nodal Sets for Dirac and Laplace Operators. Zbl 0888.47028
Bär, Christian
26
1997
Harmonic spinors for twisted Dirac operators. Zbl 0889.53025
Bär, Christian
5
1997
Metrics with harmonic spinors. Zbl 0867.53037
Bär, C.
40
1996
The Dirac operator on space forms of positive curvature. Zbl 0848.58046
Bär, Christian
35
1996
A remark on positively curved 4-manifolds. Zbl 0796.53039
Bär, Christian
1
1994
Real Killing spinors and holonomy. Zbl 0778.53037
Bär, Christian
129
1993
Lower eigenvalue estimates for Dirac operators. Zbl 0741.58046
Bär, Christian
33
1992
Harmonic spinors on Riemann surfaces. Zbl 0763.30017
Bär, Christian; Schmutz, Paul
18
1992
The Dirac operator on homogeneous spaces and its spectrum on 3- dimensional lens spaces. Zbl 0786.53030
Bär, Christian
18
1992
Upper eigenvalue estimates for Dirac operators. Zbl 0770.53026
Bär, Christian
2
1992
The Dirac fundamental tone of the hyperbolic space. Zbl 0757.53020
Bär, Christian
1
1992
The spectrum of Dirac operators. (Das Spektrum von Dirac-Operatoren.) Zbl 0748.53022
Bär, Christian
5
1990
all top 5

Cited by 587 Authors

20 Dappiaggi, Claudio
18 Ammann, Bernd Eberhard
17 Bär, Christian
16 Ginoux, Nicolas
16 Moroianu, Andrei
12 Benini, Marco
12 Habib, Georges
12 Nakad, Roger
11 Roth, Julien
11 Schenkel, Alexander
10 Moroianu, Sergiu
10 Semmelmann, Uwe
9 Branding, Volker
9 Große, Nadine
9 Pinamonti, Nicola
8 Drago, Nicolò
7 Chen, Yongfa
7 Fewster, Christopher John
7 Friedrich, Thomas
7 Hijazi, Oussama
7 Humbert, Emmanuel
7 Lee, Yoonweon
7 Ludewig, Matthias
7 Murro, Simone
7 Raulot, Simon
7 Verch, Rainer
6 Bayard, Pierre
6 Conti, Diego
6 Fredenhagen, Klaus
6 Hack, Thomas-Paul
6 Jost, Jürgen
6 Sati, Hisham
6 Strohmaier, Alexander
6 Zhu, Miaomiao
5 Chen, Qun
5 Finster, Felix
5 Fröb, Markus B.
5 Kim, Eui Chul
5 Lawn, Marie-Amélie
5 Montiel, Sebastián
5 Rejzner, Kasia
5 Salamon, Simon Montague
5 Sanders, Ko
5 Shahbazi, Carlos S.
5 Sitarz, Andrzej
5 Zahn, Jochen
4 Baum, Helga
4 Chen, Daguang
4 Dabrowski, Ludwik
4 Dahl, Mattias
4 Kath, Ines
4 Kraus, Margarita
4 Lauret, Emilio A.
4 Lazaroiu, Calin Iuliu
4 Leistner, Thomas
4 Wrochna, Michał
4 Wu, Ruijun
4 Zabzine, Maxim
3 Agricola, Ilka
3 Alexandrov, Bogdan
3 Arrizabalaga, Naiara
3 Ballmann, Hans Werner
3 Braverman, Maxim
3 Cekić, Mihajlo
3 Chrysikos, Ioannis
3 Coriasco, Sandro
3 Cortés, Vicente
3 El Chami, Fida
3 Enciso, Alberto
3 Goette, Sebastian
3 Grady, Daniel
3 Hollands, Stefan
3 Homma, Yasushi
3 Huang, Rung-Tzung
3 Kamran, Niky
3 Le Treust, Loïc
3 Loya, Paul A.
3 Marcolli, Matilde
3 Morel, Bertrand
3 Müller, Olaf
3 Nistor, Victor
3 Nowaczyk, Nikolai
3 Ourmiéres-Bonafos, Thomas
3 Petersen, Oliver Lindblad
3 Pfäffle, Frank Jochen
3 Pigola, Stefano
3 Qiu, Jian
3 Raymond, Nicolas
3 Setti, Alberto G.
3 Shi, Pengshuai
3 Vassiliev, Dmitri G.
3 Wang, Guofang
3 Waterstraat, Nils
3 Witt, Frederik
3 Zelditch, Steve
2 Agranovsky, Mark L.
2 Alekseevskiĭ, Dmitriĭ Vladimirovich
2 Amann, Manuel
2 Avramidi, Ivan G.
2 Bakas, Ioannis
...and 487 more Authors
all top 5

Cited in 130 Serials

77 Journal of Geometry and Physics
64 Communications in Mathematical Physics
36 Annals of Global Analysis and Geometry
23 Journal of Mathematical Physics
21 Differential Geometry and its Applications
21 Annales Henri Poincaré
20 Mathematische Zeitschrift
20 Journal of High Energy Physics
18 Letters in Mathematical Physics
16 The Journal of Geometric Analysis
14 Reviews in Mathematical Physics
12 Transactions of the American Mathematical Society
11 Calculus of Variations and Partial Differential Equations
10 Classical and Quantum Gravity
10 Journal of Functional Analysis
9 Advances in Mathematics
9 Mathematical Physics, Analysis and Geometry
9 International Journal of Geometric Methods in Modern Physics
8 Nuclear Physics. B
8 Manuscripta Mathematica
8 International Journal of Mathematics
6 Journal of Noncommutative Geometry
5 Journal of Mathematical Analysis and Applications
5 Annales de l’Institut Fourier
5 Duke Mathematical Journal
5 Results in Mathematics
5 Advances in Applied Clifford Algebras
5 Comptes Rendus. Mathématique. Académie des Sciences, Paris
4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
4 Annali di Matematica Pura ed Applicata. Serie Quarta
4 Mathematische Annalen
4 Potential Analysis
4 Geometry & Topology
3 International Journal of Modern Physics A
3 General Relativity and Gravitation
3 Fortschritte der Physik
3 Compositio Mathematica
3 Geometriae Dedicata
3 Journal für die Reine und Angewandte Mathematik
3 Proceedings of the American Mathematical Society
3 Geometric and Functional Analysis. GAFA
3 Communications in Partial Differential Equations
2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
2 Archiv der Mathematik
2 Chinese Annals of Mathematics. Series B
2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
2 Journal de Mathématiques Pures et Appliquées. Neuvième Série
2 Vietnam Journal of Mathematics
2 Journal of the European Mathematical Society (JEMS)
2 Communications in Contemporary Mathematics
2 Central European Journal of Mathematics
2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
2 Foundations of Physics
2 Frontiers of Mathematics in China
2 Journal of Homotopy and Related Structures
2 Journal of Topology and Analysis
2 São Paulo Journal of Mathematical Sciences
2 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics
2 Science China. Mathematics
2 Journal of Spectral Theory
1 Modern Physics Letters A
1 Archive for Rational Mechanics and Analysis
1 Inverse Problems
1 Mathematical Notes
1 Nonlinearity
1 Physics Letters. A
1 Physics Letters. B
1 Physics Reports
1 Reports on Mathematical Physics
1 Rocky Mountain Journal of Mathematics
1 Theoretical and Mathematical Physics
1 Annales Polonici Mathematici
1 Canadian Journal of Mathematics
1 Illinois Journal of Mathematics
1 Indiana University Mathematics Journal
1 Journal of Differential Equations
1 Journal of Differential Geometry
1 Journal of Geometry
1 Journal of the London Mathematical Society. Second Series
1 Journal of the Mathematical Society of Japan
1 Mathematische Nachrichten
1 Memoirs of the American Mathematical Society
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Osaka Journal of Mathematics
1 Pacific Journal of Mathematics
1 Proceedings of the London Mathematical Society. Third Series
1 Rendiconti del Circolo Matemàtico di Palermo. Serie II
1 Topology and its Applications
1 Revista Matemática Iberoamericana
1 Annals of Physics
1 Expositiones Mathematicae
1 Indagationes Mathematicae. New Series
1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
1 Experimental Mathematics
1 International Journal of Modern Physics D
1 Russian Journal of Mathematical Physics
1 Journal of Lie Theory
1 Selecta Mathematica. New Series
1 Advances in Differential Equations
1 Discrete and Continuous Dynamical Systems
...and 30 more Serials
all top 5

Cited in 50 Fields

360 Differential geometry (53-XX)
268 Global analysis, analysis on manifolds (58-XX)
179 Quantum theory (81-XX)
130 Partial differential equations (35-XX)
98 Relativity and gravitational theory (83-XX)
52 Manifolds and cell complexes (57-XX)
50 Functional analysis (46-XX)
22 Several complex variables and analytic spaces (32-XX)
17 Operator theory (47-XX)
15 Algebraic geometry (14-XX)
13 Mechanics of particles and systems (70-XX)
11 Topological groups, Lie groups (22-XX)
10 Ordinary differential equations (34-XX)
9 Calculus of variations and optimal control; optimization (49-XX)
9 Algebraic topology (55-XX)
9 Statistical mechanics, structure of matter (82-XX)
8 \(K\)-theory (19-XX)
8 Functions of a complex variable (30-XX)
8 Dynamical systems and ergodic theory (37-XX)
7 Nonassociative rings and algebras (17-XX)
6 Number theory (11-XX)
6 Probability theory and stochastic processes (60-XX)
4 Associative rings and algebras (16-XX)
4 Real functions (26-XX)
4 Approximations and expansions (41-XX)
4 Geometry (51-XX)
4 Astronomy and astrophysics (85-XX)
3 General and overarching topics; collections (00-XX)
3 Combinatorics (05-XX)
3 Category theory; homological algebra (18-XX)
3 Measure and integration (28-XX)
3 Difference and functional equations (39-XX)
3 Harmonic analysis on Euclidean spaces (42-XX)
3 Fluid mechanics (76-XX)
2 Linear and multilinear algebra; matrix theory (15-XX)
2 Potential theory (31-XX)
2 Abstract harmonic analysis (43-XX)
2 Integral transforms, operational calculus (44-XX)
2 General topology (54-XX)
2 Numerical analysis (65-XX)
2 Optics, electromagnetic theory (78-XX)
2 Information and communication theory, circuits (94-XX)
1 Commutative algebra (13-XX)
1 Group theory and generalizations (20-XX)
1 Special functions (33-XX)
1 Integral equations (45-XX)
1 Computer science (68-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 Biology and other natural sciences (92-XX)

Citations by Year

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