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## Huisken, Gerhard

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 Author ID: huisken.gerhard Published as: Huisken, G.; Huisken, Gerhard Homepage: https://www.mfo.de/about-the-institute/staff/prof.-dr.-gerhard-huisken External Links: MGP · Wikidata · GND
 Documents Indexed: 56 Publications since 1983, including 2 Books Biographic References: 1 Publication
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#### Co-Authors

 25 single-authored 7 Ecker, Klaus 5 Ilmanen, Thomas 5 Sinestrari, Carlo 4 Brendle, Simon 2 Arnlind, Joakim 2 De Lellis, Camillo 2 Dierkes, Ulrich 2 Dziuk, Gerhard 2 McCann, Robert J. 1 Alberti, Giovanni 1 Elliott, Charles M. 1 Hoppe, Jens 1 Hutchinson, John Edward 1 Jerrard, Robert Leon 1 Klingenberg, Wilhelm jun. 1 Kornhuber, Ralf 1 Polden, Alexander 1 Yau, Shing-Tung
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#### Serials

 8 Journal of Differential Geometry 6 Inventiones Mathematicae 5 Oberwolfach Reports 2 Mathematische Zeitschrift 2 Pacific Journal of Mathematics 1 Bulletin of the Australian Mathematical Society 1 Communications in Mathematical Physics 1 Letters in Mathematical Physics 1 Acta Mathematica 1 Duke Mathematical Journal 1 Journal of Differential Equations 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 IMRN. International Mathematics Research Notices 1 Calculus of Variations and Partial Differential Equations 1 Mathematical Research Letters 1 Documenta Mathematica 1 The Asian Journal of Mathematics 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Proceedings of the Centre for Mathematics and its Applications, Australian National University
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#### Fields

 47 Differential geometry (53-XX) 21 Partial differential equations (35-XX) 15 Global analysis, analysis on manifolds (58-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 7 Relativity and gravitational theory (83-XX) 6 General and overarching topics; collections (00-XX) 2 Convex and discrete geometry (52-XX) 2 Manifolds and cell complexes (57-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Numerical analysis (65-XX) 1 Fluid mechanics (76-XX)

#### Citations contained in zbMATH

43 Publications have been cited 1,947 times in 1,139 Documents Cited by Year
Flow by mean curvature of convex surfaces into spheres. Zbl 0556.53001
Huisken, Gerhard
1984
Asymptotic behavior for singularities of the mean curvature flow. Zbl 0694.53005
Huisken, Gerhard
1990
The inverse mean curvature flow and the Riemannian Penrose inequality. Zbl 1055.53052
Huisken, Gerhard; Ilmanen, Tom
2001
Mean curvature evolution of entire graphs. Zbl 0696.53036
Ecker, Klaus; Huisken, Gerhard
1989
Convexity estimates for mean curvature flow and singularities of mean convex surfaces. Zbl 0992.53051
Huisken, Gerhard; Sinestrari, Carlo
1999
Interior estimates for hypersurfaces moving by mean curvature. Zbl 0707.53008
Ecker, Klaus; Huisken, Gerhard
1991
The volume preserving mean curvature flow. Zbl 0621.53007
Huisken, Gerhard
1987
Mean curvature flow singularities for mean convex surfaces. Zbl 0992.53052
Huisken, Gerhard; Sinestrari, Carlo
1999
Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature. Zbl 0589.53058
Huisken, Gerhard
1986
Geometric evolution equations for hypersurfaces. Zbl 0942.35047
Huisken, Gerhard; Polden, Alexander
1999
Ricci deformation of the metric on a Riemannian manifold. Zbl 0606.53026
Huisken, Gerhard
1985
Local and global behaviour of hypersurfaces moving by mean curvature. Zbl 0791.58090
Huisken, Gerhard
1993
Non-parametric mean curvature evolution with boundary conditions. Zbl 0686.34013
Huisken, Gerhard
1989
Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature. Zbl 0858.53071
Huisken, Gerhard; Yau, Shing-Tung
1996
Mean curvature flow with surgeries of two-convex hypersurfaces. Zbl 1170.53042
Huisken, Gerhard; Sinestrari, Carlo
2009
A distance comparison principle for evolving curves. Zbl 0931.53032
Huisken, Gerhard
1998
Parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes. Zbl 0721.53055
Ecker, Klaus; Huisken, Gerhard
1991
Higher regularity of the inverse mean curvature flow. Zbl 1161.53058
Huisken, Gerhard; Ilmanen, Tom
2008
The Riemannian Penrose inequality. Zbl 0905.53043
Huisken, G.; Ilmanen, T.
1997
Deforming hypersurfaces of the sphere by their mean curvature. Zbl 0626.53039
Huisken, Gerhard
1987
A Bernstein result for minimal graphs of controlled growth. Zbl 0696.53002
Ecker, Klaus; Huisken, Gerhard
1990
Mean curvature flow with surgery of mean convex surfaces in $$\mathbb R^3$$. Zbl 1381.53113
Brendle, Simon; Huisken, Gerhard
2016
Convex ancient solutions of the mean curvature flow. Zbl 1332.53085
Huisken, Gerhard; Sinestrari, Carlo
2015
The $$n$$-dimensional analogue of the catenary: Existence and non-existence. Zbl 0652.49029
Dierkes, Ulrich; Huisken, Gerhard
1990
Immersed hypersurfaces with constant Weingarten curvature. Zbl 0643.53043
Ecker, Klaus; Huisken, Gerhard
1989
Multi-linear formulation of differential geometry and matrix regularizations. Zbl 1252.53024
Arnlind, Joakim; Hoppe, Jens; Huisken, Gerhard
2012
Ancient solutions to the Ricci flow with pinched curvature. Zbl 1219.53062
Brendle, Simon; Huisken, Gerhard; Sinestrari, Carlo
2011
Flow of real hypersurfaces by the trace of the Levi form. Zbl 0956.32034
Huisken, Gerhard; Klingenberg, Wilhelm
1999
Interior curvature estimates for hypersurfaces of prescribed mean curvature. Zbl 0683.53007
Ecker, Klaus; Huisken, Gerhard
1989
Capillary surfaces over obstacles. Zbl 0561.49009
Huisken, Gerhard
1985
Pseudo-Riemannian geometry in terms of multi-linear brackets. Zbl 1308.53123
Arnlind, Joakim; Huisken, Gerhard
2014
A fully nonlinear flow for two-convex hypersurfaces in Riemannian manifolds. Zbl 1386.53079
Brendle, Simon; Huisken, Gerhard
2017
Evolution of hypersurfaces by their curvature in Riemannian manifolds. Zbl 0912.53038
Huisken, Gerhard
1998
Mean curvature flow with surgery of mean convex surfaces in three-manifolds. Zbl 1407.53061
Brendle, Simon; Huisken, Gerhard
2018
Geometric concepts for the mass in general relativity. Zbl 1049.83514
Huisken, Gerhard
1999
The $$n$$-dimensional analogue of the catenary: Prescribed area. Zbl 0933.35072
Dierkes, Ulrich; Huisken, Gerhard
1996
Calculus of variations. Abstracts from the workshop held July 22–28, 2012. Zbl 1349.00130
De Lellis, Camillo (ed.); Huisken, Gerhard (ed.); Jerrard, Robert L. (ed.)
2012
Geometric partial differential equations: theory, numerics and applications. Abstracts from the workshop held November 27 – December 3, 2011. Zbl 1349.00149
Dziuk, Gerhard (ed.); Elliott, Charles M. (ed.); Huisken, Gerhard (ed.); Kornhuber, Ralf (ed.)
2011
Energy inequalities for isolated systems and hypersurfaces moving by their curvature. Zbl 1032.83018
Huisken, Gerhard; Ilmanen, Tom
2002
Singularities of the mean curvature flow. Zbl 0891.53039
Huisken, Gerhard
1997
Mean curvature evolution of closed hypersurfaces. Zbl 0891.53038
Huisken, Gerhard
1997
Capillary surfaces in negative gravitational fields. Zbl 0506.49005
Huisken, Gerhard
1984
On pendent drops in a capillary tube. Zbl 0521.76103
Huisken, G.
1983
Mean curvature flow with surgery of mean convex surfaces in three-manifolds. Zbl 1407.53061
Brendle, Simon; Huisken, Gerhard
2018
A fully nonlinear flow for two-convex hypersurfaces in Riemannian manifolds. Zbl 1386.53079
Brendle, Simon; Huisken, Gerhard
2017
Mean curvature flow with surgery of mean convex surfaces in $$\mathbb R^3$$. Zbl 1381.53113
Brendle, Simon; Huisken, Gerhard
2016
Convex ancient solutions of the mean curvature flow. Zbl 1332.53085
Huisken, Gerhard; Sinestrari, Carlo
2015
Pseudo-Riemannian geometry in terms of multi-linear brackets. Zbl 1308.53123
Arnlind, Joakim; Huisken, Gerhard
2014
Multi-linear formulation of differential geometry and matrix regularizations. Zbl 1252.53024
Arnlind, Joakim; Hoppe, Jens; Huisken, Gerhard
2012
Calculus of variations. Abstracts from the workshop held July 22–28, 2012. Zbl 1349.00130
De Lellis, Camillo (ed.); Huisken, Gerhard (ed.); Jerrard, Robert L. (ed.)
2012
Ancient solutions to the Ricci flow with pinched curvature. Zbl 1219.53062
Brendle, Simon; Huisken, Gerhard; Sinestrari, Carlo
2011
Geometric partial differential equations: theory, numerics and applications. Abstracts from the workshop held November 27 – December 3, 2011. Zbl 1349.00149
Dziuk, Gerhard (ed.); Elliott, Charles M. (ed.); Huisken, Gerhard (ed.); Kornhuber, Ralf (ed.)
2011
Mean curvature flow with surgeries of two-convex hypersurfaces. Zbl 1170.53042
Huisken, Gerhard; Sinestrari, Carlo
2009
Higher regularity of the inverse mean curvature flow. Zbl 1161.53058
Huisken, Gerhard; Ilmanen, Tom
2008
Energy inequalities for isolated systems and hypersurfaces moving by their curvature. Zbl 1032.83018
Huisken, Gerhard; Ilmanen, Tom
2002
The inverse mean curvature flow and the Riemannian Penrose inequality. Zbl 1055.53052
Huisken, Gerhard; Ilmanen, Tom
2001
Convexity estimates for mean curvature flow and singularities of mean convex surfaces. Zbl 0992.53051
Huisken, Gerhard; Sinestrari, Carlo
1999
Mean curvature flow singularities for mean convex surfaces. Zbl 0992.53052
Huisken, Gerhard; Sinestrari, Carlo
1999
Geometric evolution equations for hypersurfaces. Zbl 0942.35047
Huisken, Gerhard; Polden, Alexander
1999
Flow of real hypersurfaces by the trace of the Levi form. Zbl 0956.32034
Huisken, Gerhard; Klingenberg, Wilhelm
1999
Geometric concepts for the mass in general relativity. Zbl 1049.83514
Huisken, Gerhard
1999
A distance comparison principle for evolving curves. Zbl 0931.53032
Huisken, Gerhard
1998
Evolution of hypersurfaces by their curvature in Riemannian manifolds. Zbl 0912.53038
Huisken, Gerhard
1998
The Riemannian Penrose inequality. Zbl 0905.53043
Huisken, G.; Ilmanen, T.
1997
Singularities of the mean curvature flow. Zbl 0891.53039
Huisken, Gerhard
1997
Mean curvature evolution of closed hypersurfaces. Zbl 0891.53038
Huisken, Gerhard
1997
Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature. Zbl 0858.53071
Huisken, Gerhard; Yau, Shing-Tung
1996
The $$n$$-dimensional analogue of the catenary: Prescribed area. Zbl 0933.35072
Dierkes, Ulrich; Huisken, Gerhard
1996
Local and global behaviour of hypersurfaces moving by mean curvature. Zbl 0791.58090
Huisken, Gerhard
1993
Interior estimates for hypersurfaces moving by mean curvature. Zbl 0707.53008
Ecker, Klaus; Huisken, Gerhard
1991
Parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes. Zbl 0721.53055
Ecker, Klaus; Huisken, Gerhard
1991
Asymptotic behavior for singularities of the mean curvature flow. Zbl 0694.53005
Huisken, Gerhard
1990
A Bernstein result for minimal graphs of controlled growth. Zbl 0696.53002
Ecker, Klaus; Huisken, Gerhard
1990
The $$n$$-dimensional analogue of the catenary: Existence and non-existence. Zbl 0652.49029
Dierkes, Ulrich; Huisken, Gerhard
1990
Mean curvature evolution of entire graphs. Zbl 0696.53036
Ecker, Klaus; Huisken, Gerhard
1989
Non-parametric mean curvature evolution with boundary conditions. Zbl 0686.34013
Huisken, Gerhard
1989
Immersed hypersurfaces with constant Weingarten curvature. Zbl 0643.53043
Ecker, Klaus; Huisken, Gerhard
1989
Interior curvature estimates for hypersurfaces of prescribed mean curvature. Zbl 0683.53007
Ecker, Klaus; Huisken, Gerhard
1989
The volume preserving mean curvature flow. Zbl 0621.53007
Huisken, Gerhard
1987
Deforming hypersurfaces of the sphere by their mean curvature. Zbl 0626.53039
Huisken, Gerhard
1987
Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature. Zbl 0589.53058
Huisken, Gerhard
1986
Ricci deformation of the metric on a Riemannian manifold. Zbl 0606.53026
Huisken, Gerhard
1985
Capillary surfaces over obstacles. Zbl 0561.49009
Huisken, Gerhard
1985
Flow by mean curvature of convex surfaces into spheres. Zbl 0556.53001
Huisken, Gerhard
1984
Capillary surfaces in negative gravitational fields. Zbl 0506.49005
Huisken, Gerhard
1984
On pendent drops in a capillary tube. Zbl 0521.76103
Huisken, G.
1983
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#### Cited by 1,076 Authors

 24 Brendle, Simon 16 Miao, Pengzi 15 Li, Haizhong 14 Novaga, Matteo 14 Xin, Yuanlong 13 Andrews, Ben 13 Colding, Tobias Holck 12 Huisken, Gerhard 12 Li, Guanghan 12 Li, Jiayu 12 Sinestrari, Carlo 12 Xu, Hongwei 11 McCoy, James Alexander 11 Smoczyk, Knut 11 Wheeler, Glen E. 10 Arroja Neves, André 10 Bellettini, Giovanni 10 Minicozzi, William Philip II 10 Miquel, Vicente 10 Shi, Yuguang 10 Wang, Mu-Tao 10 Wei, Yong 9 Liu, Yannan 9 Mantegazza, Carlo 9 Schulze, Felix 9 Sheng, Weimin 9 Tam, Luen-Fai 9 Wang, Guofang 8 Chen, Jingyi 8 Ding, Qi 8 Ecker, Klaus 8 Eichmair, Michael 8 Han, Xiaoli 8 Haslhofer, Robert 8 Khuri, Marcus A. 8 Nguyen, Xuan Hien 8 Scheuer, Julian 8 Sesum, Natasa 8 Wheeler, Valentina-Mira 8 Yau, Shing-Tung 8 Zhao, En-Tao 7 Bray, Hubert L. 7 Cheng, Qingming 7 Chodosh, Otis 7 Guan, Pengfei 7 Jauregui, Jeffrey L. 7 Lambert, Ben 7 Mazzieri, Lorenzo 7 Tian, Gang 7 Uguzzoni, Francesco 7 Wang, Xiaoliu 7 Yang, Ling 6 Arnlind, Joakim 6 Chambolle, Antonin 6 Fu, Haiping 6 Garcke, Harald 6 Girão, Frederico 6 Hershkovits, Or 6 Jian, Huai-Yu 6 Kim, Daehwan 6 Kröner, Heiko 6 Li, Xingxiao 6 Mao, Jing 6 Omari, Pierpaolo 6 Pyo, Juncheol 6 Tonegawa, Yoshihiro 6 Tsai, Dong-Ho 6 White, Brian Cabell 6 Wu, Jie 6 Yang, LiuQing 6 Zhou, Detang 5 Cheng, Xu 5 Chu, Yawei 5 Drugan, Gregory 5 Ge, Yuxin 5 Giga, Yoshikazu 5 Huang, Guangyue 5 Huang, Lan-Hsuan 5 Ju, Hongjie 5 Langford, Mat 5 Lee, Dan Archibald 5 Lopes de Lima, Levi 5 Lopez Camino, Rafael 5 López-Gómez, Julián 5 Lopez, Rafael Beltran 5 Ma, Li 5 Metzger, Jan 5 Ni, Lei 5 Pipoli, Giuseppe 5 Rigoli, Marco 5 Schäfer, Lars 5 Soner, Halil Mete 5 Sun, Jun 5 Wu, Chuanxi 5 Xiong, Changwei 5 Zhu, Jonathan J. H. 4 Agostiniani, Virginia 4 Allen, Brian Michael 4 Angenent, Sigurd Bernardus 4 Bonfiglioli, Andrea ...and 976 more Authors
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#### Cited in 190 Serials

 84 Calculus of Variations and Partial Differential Equations 62 The Journal of Geometric Analysis 53 Proceedings of the American Mathematical Society 50 Transactions of the American Mathematical Society 37 Advances in Mathematics 34 Journal of Differential Equations 32 Communications in Mathematical Physics 29 Inventiones Mathematicae 26 Journal für die Reine und Angewandte Mathematik 24 Mathematische Zeitschrift 23 Journal of Mathematical Analysis and Applications 22 Journal of Geometry and Physics 21 Geometriae Dedicata 20 Annals of Global Analysis and Geometry 19 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 18 Mathematische Annalen 18 Annales Henri Poincaré 17 Journal of Functional Analysis 17 Manuscripta Mathematica 17 International Journal of Mathematics 15 Communications in Contemporary Mathematics 14 Differential Geometry and its Applications 13 Chinese Annals of Mathematics. Series B 12 General Relativity and Gravitation 12 Journal of Mathematical Physics 11 Archive for Rational Mechanics and Analysis 11 Communications in Partial Differential Equations 11 Science China. Mathematics 10 Results in Mathematics 9 Journal of the American Mathematical Society 9 Bulletin of the American Mathematical Society. New Series 9 Acta Mathematica Sinica. English Series 9 Frontiers of Mathematics in China 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Duke Mathematical Journal 8 Geometry & Topology 8 Annals of Mathematics. Second Series 8 Journal of Evolution Equations 7 Classical and Quantum Gravity 7 Communications on Pure and Applied Mathematics 7 Archiv der Mathematik 7 Journal of Geometry 7 Pacific Journal of Mathematics 7 Geometric and Functional Analysis. GAFA 7 NoDEA. Nonlinear Differential Equations and Applications 7 Discrete and Continuous Dynamical Systems 7 Geometric Flows 6 Bulletin of the Australian Mathematical Society 6 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 6 SIAM Journal on Mathematical Analysis 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Potential Analysis 5 Mathematical Physics, Analysis and Geometry 4 Journal of Computational Physics 4 Publications Mathématiques 4 Mathematische Nachrichten 4 Numerische Mathematik 4 Physica D 4 Applied Mathematics. Series B (English Edition) 4 Journal of High Energy Physics 3 Letters in Mathematical Physics 3 Mathematical Methods in the Applied Sciences 3 Nuclear Physics. B 3 Acta Mathematica 3 The Annals of Probability 3 Journal of the Korean Mathematical Society 3 Memoirs of the American Mathematical Society 3 Revista Matemática Iberoamericana 3 Journal of Mathematical Sciences (New York) 3 Bulletin des Sciences Mathématiques 3 Abstract and Applied Analysis 3 Living Reviews in Relativity 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Communications on Pure and Applied Analysis 3 Milan Journal of Mathematics 3 Mediterranean Journal of Mathematics 3 Advances in Calculus of Variations 3 Nonlinear Analysis. Theory, Methods & Applications 2 Israel Journal of Mathematics 2 Journal d’Analyse Mathématique 2 Journal of Fluid Mechanics 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Annales de l’Institut Fourier 2 Indiana University Mathematics Journal 2 Journal of Computational and Applied Mathematics 2 Monatshefte für Mathematik 2 Osaka Journal of Mathematics 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Proceedings of the Japan Academy. Series A 2 SIAM Journal on Numerical Analysis 2 Bulletin of the Korean Mathematical Society 2 Computer Aided Geometric Design 2 Probability Theory and Related Fields 2 Applied Mathematics Letters 2 Science in China. Series A 2 European Journal of Applied Mathematics 2 Journal of Elasticity 2 Electronic Research Announcements of the American Mathematical Society 2 Analysis (München) ...and 90 more Serials
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#### Cited in 47 Fields

 943 Differential geometry (53-XX) 415 Partial differential equations (35-XX) 167 Global analysis, analysis on manifolds (58-XX) 124 Relativity and gravitational theory (83-XX) 74 Calculus of variations and optimal control; optimization (49-XX) 36 Numerical analysis (65-XX) 27 Convex and discrete geometry (52-XX) 18 Several complex variables and analytic spaces (32-XX) 16 Manifolds and cell complexes (57-XX) 13 Probability theory and stochastic processes (60-XX) 13 Mechanics of deformable solids (74-XX) 12 Quantum theory (81-XX) 11 Dynamical systems and ergodic theory (37-XX) 11 Fluid mechanics (76-XX) 9 Potential theory (31-XX) 8 Measure and integration (28-XX) 8 Biology and other natural sciences (92-XX) 7 Operator theory (47-XX) 7 Computer science (68-XX) 6 Algebraic geometry (14-XX) 6 Ordinary differential equations (34-XX) 6 Functional analysis (46-XX) 6 Geometry (51-XX) 5 Abstract harmonic analysis (43-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 General and overarching topics; collections (00-XX) 4 Real functions (26-XX) 4 Mechanics of particles and systems (70-XX) 2 History and biography (01-XX) 2 Nonassociative rings and algebras (17-XX) 2 Topological groups, Lie groups (22-XX) 2 Functions of a complex variable (30-XX) 2 Algebraic topology (55-XX) 2 Operations research, mathematical programming (90-XX) 1 Combinatorics (05-XX) 1 General algebraic systems (08-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX)

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