×
Compute Distance To:
Author ID: katz.mikhail-g Recent zbMATH articles by "Katz, Mikhail G."
Published as: Katz, Mikhail G.; Katz, Mikhail; Katz, M.; Katz, M. G.
Homepage: http://u.cs.biu.ac.il/~katzmik/
External Links: MGP · Wikidata · MathOverflow · dblp · GND · IdRef
Documents Indexed: 101 Publications since 1983, including 1 Book
3 Further Contributions
Reviewing Activity: 50 Reviews
Co-Authors: 52 Co-Authors with 83 Joint Publications
877 Co-Co-Authors
all top 5

Serials

14 Foundations of Science
6 Geometriae Dedicata
5 Geometric and Functional Analysis. GAFA
5 Open Mathematics
4 Israel Journal of Mathematics
3 Proceedings of the American Mathematical Society
3 Real Analysis Exchange
3 Notices of the American Mathematical Society
3 Matematychni Studiï
2 Communications on Pure and Applied Mathematics
2 Commentarii Mathematici Helvetici
2 Duke Mathematical Journal
2 Journal of Differential Geometry
2 Journal of Geometry
2 Transactions of the American Mathematical Society
2 The Journal of Geometric Analysis
2 Philosophia Mathematica. Series III
2 Logica Universalis
2 Journal of Topology and Analysis
2 Perspectives on Science
2 British Journal for the History of Mathematics
1 American Mathematical Monthly
1 The Mathematical Intelligencer
1 Annales de l’Institut Fourier
1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
1 Fundamenta Mathematicae
1 Journal of the London Mathematical Society. Second Series
1 The Journal of Symbolic Logic
1 Mathematische Annalen
1 Notre Dame Journal of Formal Logic
1 Pacific Journal of Mathematics
1 The Quarterly Journal of Mathematics. Oxford Second Series
1 Topology and its Applications
1 Ergodic Theory and Dynamical Systems
1 Annals of Pure and Applied Logic
1 Discrete & Computational Geometry
1 IMRN. International Mathematics Research Notices
1 Historia Mathematica
1 Comptes Rendus de l’Académie des Sciences. Série I
1 Experimental Mathematics
1 Communications in Analysis and Geometry
1 Mathematical Research Letters
1 Geometry & Topology
1 Erkenntnis
1 Algebraic & Geometric Topology
1 Mathematical Surveys and Monographs
1 Progress in Mathematics
1 Journal of Logic and Analysis
1 The Review of Symbolic Logic
1 Quantum Studies: Mathematics and Foundations
1 Modern Birkhäuser Classics

Publications by Year

Citations contained in zbMATH Open

88 Publications have been cited 1,071 times in 235 Documents Cited by Year
Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu. Zbl 0953.53002
Gromov, Misha
306
1999
Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu. 3rd printing. Zbl 1113.53001
Gromov, Misha
81
2007
Systolic geometry and topology. With an appendix by Jake P. Solomon. Zbl 1149.53003
Katz, Mikhail G.
29
2007
Small values of the Lusternik-Schnirelman category for manifolds. Zbl 1152.55002
Dranishnikov, Alexander N.; Katz, Mikhail G.; Rudyak, Yuli B.
27
2008
Logarithmic growth of systole of arithmetic Riemann surfaces along congruence subgroups. Zbl 1149.53025
Katz, Mikhail G.; Schaps, Mary; Vishne, Uzi
26
2007
Leibniz’s infinitesimals: their fictionality, their modern implementations, and their foes from Berkeley to Russell and beyond. Zbl 1303.01012
Katz, Mikhail G.; Sherry, David
24
2013
The filling radius of two-point homogeneous spaces. Zbl 0529.53032
Katz, Mikhail
20
1983
Who gave you the Cauchy-Weierstrass tale? The dual history of rigorous calculus. Zbl 1279.01017
Borovik, Alexandre; Katz, Mikhail G.
20
2012
Universal volume bounds in Riemannian manifolds. Zbl 1051.53026
Croke, Christopher B.; Katz, Mikhail
18
2003
A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography. Zbl 1283.03006
Katz, Karin Usadi; Katz, Mikhail G.
17
2012
Fermat, Leibniz, Euler, and the gang: the true history of the concepts of limit and shadow. Zbl 1338.26001
Bascelli, Tiziana; Bottazzi, Emanuele; Herzberg, Frederik; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Nowik, Tahl; Sherry, David; Shnider, Steven
17
2014
Cauchy’s continuum. Zbl 1292.01028
Katz, Karin U.; Katz, Mikhail G.
16
2011
Entropy of systolically extremal surfaces and asymptotic bounds. Zbl 1097.53027
Katz, Mikhail G.; Sabourau, Stéphane
16
2005
The Morse landscape of a Riemannian disk. Zbl 0780.53035
Frankel, S.; Katz, Mikhail
15
1993
Commuting and noncommuting infinitesimals. Zbl 1280.26047
Katz, Mikhail G.; Leichtnam, Eric
15
2013
An optimal systolic inequality for \(\mathrm{CAT}(0)\) metrics in genus two. Zbl 1156.53019
Katz, Mikhail G.; Sabourau, Stéphane
15
2006
Leibniz’s laws of continuity and homogeneity. Zbl 1284.03064
Katz, Mikhail G.; Sherry, David M.
15
2012
Is mathematical history written by the victors? Zbl 1334.01010
Bair, Jacques; Błaszczyk, Piotr; Ely, Robert; Henry, Valérie; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; McGaffey, Thomas; Schaps, David M.; Sherry, David; Shnider, Steven
14
2013
An optimal Loewner-type systolic inequality and harmonic one-forms of constant norm. Zbl 1068.53027
Bangert, Victor; Katz, Mikhail
14
2004
Approaches to analysis with infinitesimals following Robinson, Nelson, and others. Zbl 1435.03094
Fletcher, Peter; Hrbacek, Karel; Kanovei, Vladimir; Katz, Mikhail G.; Lobry, Claude; Sanders, Sam
13
2017
Boundary case of equality in optimal Loewner-type inequalities. Zbl 1122.53020
Bangert, Victor; Croke, Christopher; Ivanov, Sergei V.; Katz, Mikhail G.
13
2007
\(E_7\), Wirtinger inequalities, Cayley 4-form, and homotopy. Zbl 1160.53023
Bangert, Victor; Katz, Mikhail G.; Shnider, Steven; Weinberger, Shmuel
12
2009
Generalized degree and optimal Loewner-type inequalities. Zbl 1067.53031
Ivanov, Sergei V.; Katz, Mikhail G.
12
2004
Lusternik-Schnirelmann category and systolic category of low-dimensional manifolds. Zbl 1112.55005
Katz, Mikhail G.; Rudyak, Yuli B.
12
2006
Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics. Zbl 1392.03012
Kanovei, Vladimir; Katz, Mikhail G.; Mormann, Thomas
12
2013
Stable systolic inequalities and cohomology products. Zbl 1038.53031
Bangert, Victor; Katz, Mikhail
11
2003
Ten misconceptions from the history of analysis and their debunking. Zbl 1291.01018
Błaszczyk, Piotr; Katz, Mikhail G.; Sherry, David
11
2013
A Zoll counterexample to a geodesic length conjecture. Zbl 1201.53050
Balacheff, Florent; Croke, Christopher; Katz, Mikhail G.
10
2009
Filling area conjecture and ovalless real hyperelliptic surfaces. Zbl 1082.53033
Bangert, V.; Croke, C.; Ivanov, S.; Katz, M.
10
2005
Stevin numbers and reality. Zbl 1275.01016
Katz, Karin Usadi; Katz, Mikhail G.
10
2012
Almost equal: the method of adequality from Diophantus to Fermat and beyond. Zbl 1292.01017
Katz, Mikhail G.; Schaps, David M.; Shnider, Steven
9
2013
Systolic inequalities and Massey products in simply-connected manifolds. Zbl 1165.53027
Katz, Mikhail
9
2008
Hyperelliptic surfaces are Loewner. Zbl 1090.53045
Katz, Mikhail G.; Sabourau, Stéphane
9
2006
Flat currents modulo \(p\) in metric spaces and filling radius inequalities. Zbl 1222.49057
Ambrosio, Luigi; Katz, Mikhail G.
8
2011
Differential geometry via infinitesimal displacements. Zbl 1331.26052
Nowik, Tahl; Katz, Mikhail G.
8
2015
Bi-Lipschitz approximation by finite-dimensional imbeddings. Zbl 1226.53045
Katz, Karin Usadi; Katz, Mikhail G.
8
2011
Bounding volume by systoles of 3-manifolds. Zbl 1156.53024
Katz, Mikhail G.; Rudyak, Yuli B.
8
2008
Loewner’s torus inequality with isosystolic defect. Zbl 1193.53107
Horowitz, Charles; Katz, Karin Usadi; Katz, Mikhail G.
8
2009
Filling area conjecture, optimal systolic inequalities, and the fiber class in Abelian covers. Zbl 1088.53029
Katz, Mikhail G.; Lescop, Christine
8
2005
Toward a history of mathematics focused on procedures. Zbl 1398.01005
Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; Sherry, David
8
2017
An integer construction of infinitesimals: toward a theory of eudoxus hyperreals. Zbl 1266.03074
Borovik, Alexandre; Jin, Renling; Katz, Mikhail G.
7
2012
A Cauchy-Dirac delta function. Zbl 1273.01028
Katz, Mikhail G.; Tall, David
7
2013
Cayley form, comass, and triality isomorphisms. Zbl 1206.53060
Katz, Mikhail G.; Shnider, Steve
7
2010
Systoles of 2-complexes, Reeb graph, and Grushko decomposition. Zbl 1116.57001
Katz, Mikhail G.; Rudyak, Yuli B.; Sabourau, Stéphane
6
2006
Systolic freedom of orientable manifolds. Zbl 0944.53019
Babenko, Ivan; Katz, Mikhail
6
1998
Hurwitz quaternion order and arithmetic Riemann surfaces. Zbl 1339.11094
Katz, Mikhail G.; Schaps, Mary; Vishne, Uzi
6
2011
Euler’s lute and Edwards’s oud. Zbl 1342.01017
Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Sherry, David
6
2015
Four-manifold systoles and surjectivity of period map. Zbl 1048.53031
Katz, Mikhail
5
2003
Gregory’s sixth operation. Zbl 1398.01052
Bascelli, Tiziana; Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; Nowik, Tahl; Schaps, David M.; Sherry, David
5
2018
Bolza quaternion order and asymptotics of systoles along congruence subgroups. Zbl 1411.11121
Katz, Karin; Katz, Mikhail; Schein, Michael M.; Vishne, Uzi
5
2016
Cauchy, infinitesimals and ghosts of departed quantifiers. Zbl 1476.01006
Bair, J.; Błaszczyk, P.; Ely, R.; Henry, V.; Kanovei, V.; Katz, K. U.; Katz, M. G.; Kudryk, T.; Kutateladze, S. S.; McGaffey, T.; Mormann, T.; Schaps, D. M.; Sherry, D.
4
2017
On mathematical realism and applicability of hyperreals. Zbl 1436.00032
Bottazzi, E.; Kanovei, V.; Katz, M.; Mormann, T.; Sherry, D.
4
2019
Volume of Riemannian manifolds, geometric inequalities and homotopy theory. Zbl 0967.53024
Katz, Mikhail G.; Suciu, Alexander I.
4
1999
Cauchy’s infinitesimals, his sum theorem, and foundational paradigms. Zbl 1398.01014
Bascelli, Tiziana; Błaszczyk, Piotr; Borovik, Alexandre; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; McGaffey, Thomas; Schaps, David M.; Sherry, David
4
2018
Counterexamples to isosystolic inequalities. Zbl 0842.53031
Katz, Mikhail
4
1995
A non-standard analysis of a cultural icon: the case of Paul Halmos. Zbl 1365.01032
Błaszczyk, Piotr; Borovik, Alexandre; Kanovei, Vladimir; Katz, Mikhail G.; Kudryk, Taras; Kutateladze, Semen S.; Sherry, David
4
2016
Relative systoles of relative-essential 2-complexes. Zbl 1228.53056
Katz, Karin Usadi; Katz, Mikhail G.; Sabourau, Stéphane; Shnider, Steven; Weinberger, Shmuel
4
2011
Proofs and retributions, or: why Sarah can’t take limits. Zbl 1368.00021
Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Schaps, Mary
4
2015
The Mathematical Intelligencer flunks the Olympics. Zbl 1392.03061
Gutman, Alexander E.; Katz, Mikhail G.; Kudryk, Taras S.; Kutateladze, Semen S.
4
2017
Dyck’s surfaces, systoles, and capacities. Zbl 1314.53074
Katz, Mikhail G.; Sabourau, Stéphane
4
2015
Volumes, middle-dimensional systoles, and Whitehead products. Zbl 0933.53022
Babenko, Ivan K.; Katz, Mikhail G.; Suciu, Alexander I.
3
1998
Continuity between Cauchy and Bolzano: issues of antecedents and priority. Zbl 1461.01010
Bair, Jacques; Błaszczyk, Piotr; Fuentes Guillén, Elías; Heinig, Peter; Kanovei, Vladimir; Katz, Mikhail G.
3
2020
Infinitesimal analysis without the axiom of choice. Zbl 07333022
Hrbacek, Karel; Katz, Mikhail G.
3
2021
Small oscillations of the pendulum, Euler’s method, and adequality. Zbl 1404.70014
Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Nowik, Tahl
3
2016
Minimal axiomatic frameworks for definable hyperreals with transfer. Zbl 1447.03014
Herzberg, Frederik S.; Kanovei, Vladimir; Katz, Mikhail; Lyubetsky, Vassily
3
2018
A positive function with vanishing Lebesgue integral in Zermelo-Fraenkel set theory. Zbl 1423.03180
Kanovei, Vladimir; Katz, Mikhail
3
2017
On neighborhoods of the Kuratowski imbedding beyond the first extremum of the diameter functional. Zbl 0735.46049
Katz, Mikhail
3
1991
On intersystolic inequalities in dimension 3. Zbl 0831.53046
Bérard Bergery, Lionel; Katz, Mikhail
3
1994
Controversies in the foundations of analysis: comments on Schubring’s Conflicts. Zbl 1368.01021
Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Mikhail G.; Sherry, David
3
2017
Diameter-extremal subsets of spheres. Zbl 0663.52008
Katz, Mikhail
3
1989
Toward a clarity of the extreme value theorem. Zbl 1466.26022
Katz, Karin U.; Katz, Mikhail G.; Kudryk, Taras
2
2014
Free abelian covers, short loops, stable length, and systolic inequalities. Zbl 1134.53019
Kreck, Matthias; Suciu, Alexander I.
2
2008
Obituary: Edward Nelson (1932–2014). Zbl 1323.01037
Katz, Mikhail G.; Kutateladze, Semen S.
2
2015
Fermat’s dilemma: Why did he keep mum on infinitesimals? and the European theological context. Zbl 1398.01012
Bair, Jacques; Katz, Mikhail G.; Sherry, David
2
2018
Cohomological dimension, self-linking, and systolic geometry. Zbl 1253.53039
Dranishnikov, Alexander N.; Katz, Mikhail G.; Rudyak, Yuli B.
2
2011
Jung’s theorem in complex projective geometry. Zbl 0586.53019
Katz, Mikhail
2
1985
Systolic freedom of loop space. Zbl 1048.53030
Katz, M.; Suciu, A.
2
2001
The first diameter of 3-manifolds of positive scalar curvature. Zbl 0693.53013
Katz, Mikhail
2
1988
Systolically extremal nonpositively curved surfaces are flat with finitely many singularities. Zbl 1484.53077
Katz, Mikhail G.; Sabourau, Stéphane
2
2021
Local calibration of mass and systolic geometry. Zbl 1032.53043
Katz, Mikhail
1
2002
Klein vs Mehrtens: restoring the reputation of a great modern. Zbl 1459.01017
Bair, J.; Blaszczyk, P.; Heinig, P.; Katz, M.; Schafermeyer, J. P.; Sherry, D.
1
2017
Determinantal variety and normal embedding. Zbl 1406.53048
Katz, K.; Katz, M.; Kerner, D.; Liokumovich, Y.
1
2018
Is Leibnizian calculus embeddable in first order logic? Zbl 1398.03223
Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kudryk, Taras; Mormann, Thomas; Sherry, David
1
2017
The rational filling radius of complex projective space. Zbl 0749.53032
Katz, Mikhail
1
1991
Hyperellipticity and systoles of Klein surfaces. Zbl 1267.53044
Katz, Mikhail G.; Sabourau, Stéphane
1
2012
A quantitative obstruction to collapsing surfaces. Zbl 1430.53044
Katz, Mikhail G.
1
2019
Torus cannot collapse to a segment. Zbl 1437.53029
Katz, Mikhail G.
1
2020
Internality, transfer, and infinitesimal modeling of infinite processes. Zbl 07502809
Bottazzi, Emanuele; Katz, Mikhail G.
1
2021
Infinitesimal analysis without the axiom of choice. Zbl 07333022
Hrbacek, Karel; Katz, Mikhail G.
3
2021
Systolically extremal nonpositively curved surfaces are flat with finitely many singularities. Zbl 1484.53077
Katz, Mikhail G.; Sabourau, Stéphane
2
2021
Internality, transfer, and infinitesimal modeling of infinite processes. Zbl 07502809
Bottazzi, Emanuele; Katz, Mikhail G.
1
2021
Continuity between Cauchy and Bolzano: issues of antecedents and priority. Zbl 1461.01010
Bair, Jacques; Błaszczyk, Piotr; Fuentes Guillén, Elías; Heinig, Peter; Kanovei, Vladimir; Katz, Mikhail G.
3
2020
Torus cannot collapse to a segment. Zbl 1437.53029
Katz, Mikhail G.
1
2020
On mathematical realism and applicability of hyperreals. Zbl 1436.00032
Bottazzi, E.; Kanovei, V.; Katz, M.; Mormann, T.; Sherry, D.
4
2019
A quantitative obstruction to collapsing surfaces. Zbl 1430.53044
Katz, Mikhail G.
1
2019
Gregory’s sixth operation. Zbl 1398.01052
Bascelli, Tiziana; Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; Nowik, Tahl; Schaps, David M.; Sherry, David
5
2018
Cauchy’s infinitesimals, his sum theorem, and foundational paradigms. Zbl 1398.01014
Bascelli, Tiziana; Błaszczyk, Piotr; Borovik, Alexandre; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; McGaffey, Thomas; Schaps, David M.; Sherry, David
4
2018
Minimal axiomatic frameworks for definable hyperreals with transfer. Zbl 1447.03014
Herzberg, Frederik S.; Kanovei, Vladimir; Katz, Mikhail; Lyubetsky, Vassily
3
2018
Fermat’s dilemma: Why did he keep mum on infinitesimals? and the European theological context. Zbl 1398.01012
Bair, Jacques; Katz, Mikhail G.; Sherry, David
2
2018
Determinantal variety and normal embedding. Zbl 1406.53048
Katz, K.; Katz, M.; Kerner, D.; Liokumovich, Y.
1
2018
Approaches to analysis with infinitesimals following Robinson, Nelson, and others. Zbl 1435.03094
Fletcher, Peter; Hrbacek, Karel; Kanovei, Vladimir; Katz, Mikhail G.; Lobry, Claude; Sanders, Sam
13
2017
Toward a history of mathematics focused on procedures. Zbl 1398.01005
Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; Sherry, David
8
2017
Cauchy, infinitesimals and ghosts of departed quantifiers. Zbl 1476.01006
Bair, J.; Błaszczyk, P.; Ely, R.; Henry, V.; Kanovei, V.; Katz, K. U.; Katz, M. G.; Kudryk, T.; Kutateladze, S. S.; McGaffey, T.; Mormann, T.; Schaps, D. M.; Sherry, D.
4
2017
The Mathematical Intelligencer flunks the Olympics. Zbl 1392.03061
Gutman, Alexander E.; Katz, Mikhail G.; Kudryk, Taras S.; Kutateladze, Semen S.
4
2017
A positive function with vanishing Lebesgue integral in Zermelo-Fraenkel set theory. Zbl 1423.03180
Kanovei, Vladimir; Katz, Mikhail
3
2017
Controversies in the foundations of analysis: comments on Schubring’s Conflicts. Zbl 1368.01021
Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Mikhail G.; Sherry, David
3
2017
Klein vs Mehrtens: restoring the reputation of a great modern. Zbl 1459.01017
Bair, J.; Blaszczyk, P.; Heinig, P.; Katz, M.; Schafermeyer, J. P.; Sherry, D.
1
2017
Is Leibnizian calculus embeddable in first order logic? Zbl 1398.03223
Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kudryk, Taras; Mormann, Thomas; Sherry, David
1
2017
Bolza quaternion order and asymptotics of systoles along congruence subgroups. Zbl 1411.11121
Katz, Karin; Katz, Mikhail; Schein, Michael M.; Vishne, Uzi
5
2016
A non-standard analysis of a cultural icon: the case of Paul Halmos. Zbl 1365.01032
Błaszczyk, Piotr; Borovik, Alexandre; Kanovei, Vladimir; Katz, Mikhail G.; Kudryk, Taras; Kutateladze, Semen S.; Sherry, David
4
2016
Small oscillations of the pendulum, Euler’s method, and adequality. Zbl 1404.70014
Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Nowik, Tahl
3
2016
Differential geometry via infinitesimal displacements. Zbl 1331.26052
Nowik, Tahl; Katz, Mikhail G.
8
2015
Euler’s lute and Edwards’s oud. Zbl 1342.01017
Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Sherry, David
6
2015
Proofs and retributions, or: why Sarah can’t take limits. Zbl 1368.00021
Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Schaps, Mary
4
2015
Dyck’s surfaces, systoles, and capacities. Zbl 1314.53074
Katz, Mikhail G.; Sabourau, Stéphane
4
2015
Obituary: Edward Nelson (1932–2014). Zbl 1323.01037
Katz, Mikhail G.; Kutateladze, Semen S.
2
2015
Fermat, Leibniz, Euler, and the gang: the true history of the concepts of limit and shadow. Zbl 1338.26001
Bascelli, Tiziana; Bottazzi, Emanuele; Herzberg, Frederik; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Nowik, Tahl; Sherry, David; Shnider, Steven
17
2014
Toward a clarity of the extreme value theorem. Zbl 1466.26022
Katz, Karin U.; Katz, Mikhail G.; Kudryk, Taras
2
2014
Leibniz’s infinitesimals: their fictionality, their modern implementations, and their foes from Berkeley to Russell and beyond. Zbl 1303.01012
Katz, Mikhail G.; Sherry, David
24
2013
Commuting and noncommuting infinitesimals. Zbl 1280.26047
Katz, Mikhail G.; Leichtnam, Eric
15
2013
Is mathematical history written by the victors? Zbl 1334.01010
Bair, Jacques; Błaszczyk, Piotr; Ely, Robert; Henry, Valérie; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; McGaffey, Thomas; Schaps, David M.; Sherry, David; Shnider, Steven
14
2013
Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics. Zbl 1392.03012
Kanovei, Vladimir; Katz, Mikhail G.; Mormann, Thomas
12
2013
Ten misconceptions from the history of analysis and their debunking. Zbl 1291.01018
Błaszczyk, Piotr; Katz, Mikhail G.; Sherry, David
11
2013
Almost equal: the method of adequality from Diophantus to Fermat and beyond. Zbl 1292.01017
Katz, Mikhail G.; Schaps, David M.; Shnider, Steven
9
2013
A Cauchy-Dirac delta function. Zbl 1273.01028
Katz, Mikhail G.; Tall, David
7
2013
Who gave you the Cauchy-Weierstrass tale? The dual history of rigorous calculus. Zbl 1279.01017
Borovik, Alexandre; Katz, Mikhail G.
20
2012
A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography. Zbl 1283.03006
Katz, Karin Usadi; Katz, Mikhail G.
17
2012
Leibniz’s laws of continuity and homogeneity. Zbl 1284.03064
Katz, Mikhail G.; Sherry, David M.
15
2012
Stevin numbers and reality. Zbl 1275.01016
Katz, Karin Usadi; Katz, Mikhail G.
10
2012
An integer construction of infinitesimals: toward a theory of eudoxus hyperreals. Zbl 1266.03074
Borovik, Alexandre; Jin, Renling; Katz, Mikhail G.
7
2012
Hyperellipticity and systoles of Klein surfaces. Zbl 1267.53044
Katz, Mikhail G.; Sabourau, Stéphane
1
2012
Cauchy’s continuum. Zbl 1292.01028
Katz, Karin U.; Katz, Mikhail G.
16
2011
Flat currents modulo \(p\) in metric spaces and filling radius inequalities. Zbl 1222.49057
Ambrosio, Luigi; Katz, Mikhail G.
8
2011
Bi-Lipschitz approximation by finite-dimensional imbeddings. Zbl 1226.53045
Katz, Karin Usadi; Katz, Mikhail G.
8
2011
Hurwitz quaternion order and arithmetic Riemann surfaces. Zbl 1339.11094
Katz, Mikhail G.; Schaps, Mary; Vishne, Uzi
6
2011
Relative systoles of relative-essential 2-complexes. Zbl 1228.53056
Katz, Karin Usadi; Katz, Mikhail G.; Sabourau, Stéphane; Shnider, Steven; Weinberger, Shmuel
4
2011
Cohomological dimension, self-linking, and systolic geometry. Zbl 1253.53039
Dranishnikov, Alexander N.; Katz, Mikhail G.; Rudyak, Yuli B.
2
2011
Cayley form, comass, and triality isomorphisms. Zbl 1206.53060
Katz, Mikhail G.; Shnider, Steve
7
2010
\(E_7\), Wirtinger inequalities, Cayley 4-form, and homotopy. Zbl 1160.53023
Bangert, Victor; Katz, Mikhail G.; Shnider, Steven; Weinberger, Shmuel
12
2009
A Zoll counterexample to a geodesic length conjecture. Zbl 1201.53050
Balacheff, Florent; Croke, Christopher; Katz, Mikhail G.
10
2009
Loewner’s torus inequality with isosystolic defect. Zbl 1193.53107
Horowitz, Charles; Katz, Karin Usadi; Katz, Mikhail G.
8
2009
Small values of the Lusternik-Schnirelman category for manifolds. Zbl 1152.55002
Dranishnikov, Alexander N.; Katz, Mikhail G.; Rudyak, Yuli B.
27
2008
Systolic inequalities and Massey products in simply-connected manifolds. Zbl 1165.53027
Katz, Mikhail
9
2008
Bounding volume by systoles of 3-manifolds. Zbl 1156.53024
Katz, Mikhail G.; Rudyak, Yuli B.
8
2008
Free abelian covers, short loops, stable length, and systolic inequalities. Zbl 1134.53019
Kreck, Matthias; Suciu, Alexander I.
2
2008
Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu. 3rd printing. Zbl 1113.53001
Gromov, Misha
81
2007
Systolic geometry and topology. With an appendix by Jake P. Solomon. Zbl 1149.53003
Katz, Mikhail G.
29
2007
Logarithmic growth of systole of arithmetic Riemann surfaces along congruence subgroups. Zbl 1149.53025
Katz, Mikhail G.; Schaps, Mary; Vishne, Uzi
26
2007
Boundary case of equality in optimal Loewner-type inequalities. Zbl 1122.53020
Bangert, Victor; Croke, Christopher; Ivanov, Sergei V.; Katz, Mikhail G.
13
2007
An optimal systolic inequality for \(\mathrm{CAT}(0)\) metrics in genus two. Zbl 1156.53019
Katz, Mikhail G.; Sabourau, Stéphane
15
2006
Lusternik-Schnirelmann category and systolic category of low-dimensional manifolds. Zbl 1112.55005
Katz, Mikhail G.; Rudyak, Yuli B.
12
2006
Hyperelliptic surfaces are Loewner. Zbl 1090.53045
Katz, Mikhail G.; Sabourau, Stéphane
9
2006
Systoles of 2-complexes, Reeb graph, and Grushko decomposition. Zbl 1116.57001
Katz, Mikhail G.; Rudyak, Yuli B.; Sabourau, Stéphane
6
2006
Entropy of systolically extremal surfaces and asymptotic bounds. Zbl 1097.53027
Katz, Mikhail G.; Sabourau, Stéphane
16
2005
Filling area conjecture and ovalless real hyperelliptic surfaces. Zbl 1082.53033
Bangert, V.; Croke, C.; Ivanov, S.; Katz, M.
10
2005
Filling area conjecture, optimal systolic inequalities, and the fiber class in Abelian covers. Zbl 1088.53029
Katz, Mikhail G.; Lescop, Christine
8
2005
An optimal Loewner-type systolic inequality and harmonic one-forms of constant norm. Zbl 1068.53027
Bangert, Victor; Katz, Mikhail
14
2004
Generalized degree and optimal Loewner-type inequalities. Zbl 1067.53031
Ivanov, Sergei V.; Katz, Mikhail G.
12
2004
Universal volume bounds in Riemannian manifolds. Zbl 1051.53026
Croke, Christopher B.; Katz, Mikhail
18
2003
Stable systolic inequalities and cohomology products. Zbl 1038.53031
Bangert, Victor; Katz, Mikhail
11
2003
Four-manifold systoles and surjectivity of period map. Zbl 1048.53031
Katz, Mikhail
5
2003
Local calibration of mass and systolic geometry. Zbl 1032.53043
Katz, Mikhail
1
2002
Systolic freedom of loop space. Zbl 1048.53030
Katz, M.; Suciu, A.
2
2001
Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu. Zbl 0953.53002
Gromov, Misha
306
1999
Volume of Riemannian manifolds, geometric inequalities and homotopy theory. Zbl 0967.53024
Katz, Mikhail G.; Suciu, Alexander I.
4
1999
Systolic freedom of orientable manifolds. Zbl 0944.53019
Babenko, Ivan; Katz, Mikhail
6
1998
Volumes, middle-dimensional systoles, and Whitehead products. Zbl 0933.53022
Babenko, Ivan K.; Katz, Mikhail G.; Suciu, Alexander I.
3
1998
Counterexamples to isosystolic inequalities. Zbl 0842.53031
Katz, Mikhail
4
1995
On intersystolic inequalities in dimension 3. Zbl 0831.53046
Bérard Bergery, Lionel; Katz, Mikhail
3
1994
The Morse landscape of a Riemannian disk. Zbl 0780.53035
Frankel, S.; Katz, Mikhail
15
1993
On neighborhoods of the Kuratowski imbedding beyond the first extremum of the diameter functional. Zbl 0735.46049
Katz, Mikhail
3
1991
The rational filling radius of complex projective space. Zbl 0749.53032
Katz, Mikhail
1
1991
Diameter-extremal subsets of spheres. Zbl 0663.52008
Katz, Mikhail
3
1989
The first diameter of 3-manifolds of positive scalar curvature. Zbl 0693.53013
Katz, Mikhail
2
1988
Jung’s theorem in complex projective geometry. Zbl 0586.53019
Katz, Mikhail
2
1985
The filling radius of two-point homogeneous spaces. Zbl 0529.53032
Katz, Mikhail
20
1983
all top 5

Cited by 222 Authors

61 Katz, Mikhail G.
16 Kanovei, Vladimir G.
16 Katz, Karin Usadi
13 Sabourau, Stéphane
12 Rotman, Regina
11 Błaszczyk, Piotr
11 Dranishnikov, Alexander Nikolaevich
11 Sherry, David M.
8 Nabutovsky, Alexander
6 Bottazzi, Emanuele
6 Kutateladze, Semën Samsonovich
5 Liokumovich, Yevgeny
5 Nowik, Tahl
5 Parlier, Hugo
5 Rudyak, Yuli B.
4 Bair, Jacques
4 Borovik, Alexandre V.
4 Kudryk, Taras S.
4 Sanders, Sam
4 Shnider, Steven
3 Adelstein, Ian M.
3 Croke, Christopher B.
3 El Mir, Chady
3 Guth, Lawrence David
3 Mormann, Thomas
3 Murillo, Plinio G. P.
3 Mützel, Björn
3 Papasoglu, Panos
3 Petri, Bram
3 Schaps, David M.
2 Adams, Henry
2 Ambrosio, Luigi
2 Babenko, Ivan K.
2 Balacheff, Florent
2 Bangert, Victor
2 Bascelli, Tiziana
2 Belolipetsky, Mikhail V.
2 Gendulphe, Matthieu
2 Giordano, Paolo Robuffo
2 Gómez Larrañaga, José Carlos
2 González Acuña, Francisco Javier
2 Gromov, Mikhael Leonidovich
2 Guillén, Elías Fuentes
2 Hastings, Matthew B.
2 Heil, Wolfgang H.
2 Heinig, Peter
2 Ivanov, Sergei Vladimirovich
2 Kerner, Dmitry
2 Leng, Tuo
2 Liu, Luofei
2 McGaffey, Thomas
2 Montezuma, Rafael
2 Nagy, Paul-Andi
2 Pavešić, Petar
2 Sadykov, Rustam
2 Schaps, Mary Elizabeth
2 Schein, Michael M.
2 Strom, Jeffrey A.
2 Trlifajová, Kateřina
2 Vishne, Uzi
2 Weinberger, Shmuel
2 Wenger, Stefan
2 Wilhelm, Frederick H. jun.
2 Yassine, Zeina
2 Yokota, Takumi
1 Abbondandolo, Alberto
1 Abdeljalil, Saghe
1 Adamaszek, Michal
1 Akama, Yohji
1 Akrout, Hugo
1 Ambrozio, Lucas C.
1 Anderson, Michael T.
1 Arthur, Richard T. W.
1 Azvolinsky, Arthur
1 Baglini, Lorenzo Luperi
1 Bai, Sheng
1 Barabash, G. M.
1 Baralić, Đorđe
1 Barbosa, Ezequiel R.
1 Beach, I.
1 Benci, Vieri
1 Berenguer, Joaquim
1 Błaszczyk, Zbigniew
1 Bolotov, Dmitriĭ Valer’evich
1 Boute, Raymond T.
1 Bramham, Barney
1 Bråting, Kajsa
1 Brunnbauer, Michael
1 Budzinski, Thomas
1 Capovilla, Pietro
1 Chambers, Gregory R.
1 Cheng, Herng Yi
1 Cococcioni, Marco
1 Cohn, Henry Lee
1 Colin de Verdière, Éric
1 Costa, Armindo
1 Creutz, Paul
1 Crippa, Davide
1 Curien, Nicolas
1 Davydov, Denis
...and 122 more Authors
all top 5

Cited in 90 Serials

18 Foundations of Science
14 Proceedings of the American Mathematical Society
13 Geometriae Dedicata
12 Mathematische Zeitschrift
12 Algebraic & Geometric Topology
12 Journal of Topology and Analysis
11 Geometric and Functional Analysis. GAFA
7 Transactions of the American Mathematical Society
6 Israel Journal of Mathematics
5 Duke Mathematical Journal
5 Open Mathematics
4 Differential Geometry and its Applications
4 British Journal for the History of Mathematics
3 Inventiones Mathematicae
3 Journal of Geometry
3 Manuscripta Mathematica
3 Mathematische Annalen
3 Topology and its Applications
3 Discrete & Computational Geometry
3 Revista Matemática Iberoamericana
3 Geometry & Topology
2 Archive for History of Exact Sciences
2 The Mathematical Intelligencer
2 Annales de l’Institut Fourier
2 Historia Mathematica
2 Indagationes Mathematicae. New Series
2 Matematychni Studiï
2 Logica Universalis
2 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications
2 Perspectives on Science
1 Communications in Mathematical Physics
1 Communications on Pure and Applied Mathematics
1 Discrete Mathematics
1 Journal of Mathematical Analysis and Applications
1 Journal of Mathematical Physics
1 Rocky Mountain Journal of Mathematics
1 ACM Transactions on Mathematical Software
1 Advances in Mathematics
1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
1 Commentarii Mathematici Helvetici
1 Fundamenta Mathematicae
1 Indiana University Mathematics Journal
1 International Journal for Numerical Methods in Engineering
1 Journal of Number Theory
1 The Journal of Symbolic Logic
1 Notre Dame Journal of Formal Logic
1 Osaka Journal of Mathematics
1 Real Analysis Exchange
1 Synthese
1 Annals of Pure and Applied Logic
1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
1 Journal of the American Mathematical Society
1 SIAM Journal on Discrete Mathematics
1 The Journal of Geometric Analysis
1 Linear Algebra and its Applications
1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
1 SIAM Review
1 Bulletin of the American Mathematical Society. New Series
1 Journal of Mathematical Imaging and Vision
1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
1 Experimental Mathematics
1 Calculus of Variations and Partial Differential Equations
1 Filomat
1 Boletín de la Sociedad Matemática Mexicana. Third Series
1 Electronic Research Announcements of the American Mathematical Society
1 Balkan Journal of Geometry and its Applications (BJGA)
1 Conformal Geometry and Dynamics
1 Fractional Calculus & Applied Analysis
1 Annals of Mathematics. Second Series
1 Erkenntnis
1 Journal of Nonlinear Mathematical Physics
1 International Journal of Geometric Methods in Modern Physics
1 Mediterranean Journal of Mathematics
1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
1 BSHM Bulletin
1 Groups, Geometry, and Dynamics
1 Journal of Applied and Industrial Mathematics
1 Discrete and Continuous Dynamical Systems. Series S
1 Advances in Calculus of Variations
1 Involve
1 Journal of Logic and Analysis
1 Science China. Mathematics
1 Antiquitates Mathematicae
1 Advances in Nonlinear Analysis
1 Quantum Studies: Mathematics and Foundations
1 Sahand Communications in Mathematical Analysis
1 Research in Number Theory
1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 Journal of Applied and Computational Topology
1 Electronic Research Archive
all top 5

Cited in 45 Fields

121 Differential geometry (53-XX)
37 Real functions (26-XX)
36 Manifolds and cell complexes (57-XX)
35 History and biography (01-XX)
30 Algebraic topology (55-XX)
23 Functions of a complex variable (30-XX)
22 Mathematical logic and foundations (03-XX)
19 Global analysis, analysis on manifolds (58-XX)
14 Combinatorics (05-XX)
13 Number theory (11-XX)
11 Convex and discrete geometry (52-XX)
10 Calculus of variations and optimal control; optimization (49-XX)
9 General and overarching topics; collections (00-XX)
8 Algebraic geometry (14-XX)
7 Several complex variables and analytic spaces (32-XX)
6 Quantum theory (81-XX)
5 Field theory and polynomials (12-XX)
5 Group theory and generalizations (20-XX)
5 Topological groups, Lie groups (22-XX)
5 Functional analysis (46-XX)
5 Computer science (68-XX)
4 Dynamical systems and ergodic theory (37-XX)
4 Information and communication theory, circuits (94-XX)
3 Measure and integration (28-XX)
3 Ordinary differential equations (34-XX)
3 Partial differential equations (35-XX)
3 Geometry (51-XX)
3 General topology (54-XX)
2 Associative rings and algebras (16-XX)
2 Category theory; homological algebra (18-XX)
2 Numerical analysis (65-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Commutative algebra (13-XX)
1 Linear and multilinear algebra; matrix theory (15-XX)
1 Nonassociative rings and algebras (17-XX)
1 Potential theory (31-XX)
1 Approximations and expansions (41-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Operator theory (47-XX)
1 Probability theory and stochastic processes (60-XX)
1 Mechanics of particles and systems (70-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Relativity and gravitational theory (83-XX)
1 Operations research, mathematical programming (90-XX)
1 Mathematics education (97-XX)

Citations by Year

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.