-
1
-
-
33846582942
-
-
1909 S. MUKHOPADHYAYA, New methods In the geometry of a plane arc, Bull. Calcutta Math. Soc. I, 31-37.
-
1909 S. MUKHOPADHYAYA, New methods In the geometry of a plane arc, Bull. Calcutta Math. Soc. I, 31-37.
-
-
-
-
2
-
-
33846624271
-
-
1912 ADOLF KNESER, Bemerkungen über die Anzahl der Extrema des Krümmung auf geschlossenen Kurven und über verwandte Fragen in einer nicht eucklidischen Geometrie, Festschrift Heinrich Weber, Teubner, 170-180.
-
1912 ADOLF KNESER, Bemerkungen über die Anzahl der Extrema des Krümmung auf geschlossenen Kurven und über verwandte Fragen in einer nicht eucklidischen Geometrie, Festschrift Heinrich Weber, Teubner, 170-180.
-
-
-
-
3
-
-
65749317008
-
-
1913 WILHELM BLASCHKE, Die Minimalzahl der Scheitel einer geschlossenen konvexen Kurve, Rend. Circ. Mat. Palermo 36, 220-222.
-
1913 WILHELM BLASCHKE, Die Minimalzahl der Scheitel einer geschlossenen konvexen Kurve, Rend. Circ. Mat. Palermo 36, 220-222.
-
-
-
-
4
-
-
65749320881
-
-
1914 HANS MOHRMANN, Die Minimalzahl der Scheitel einer geschlossenen konvexen Kurve, Rend. Cir. Mat. Palermo 37, 267-268.
-
1914 HANS MOHRMANN, Die Minimalzahl der Scheitel einer geschlossenen konvexen Kurve, Rend. Cir. Mat. Palermo 37, 267-268.
-
-
-
-
5
-
-
52649096200
-
-
1914 WOLFGANG VOGT, Über monotongekrümmten Kurven, J. Reine Angew. Math. 144, 239-248.
-
1914 WOLFGANG VOGT, Über monotongekrümmten Kurven, J. Reine Angew. Math. 144, 239-248.
-
-
-
-
6
-
-
33846617814
-
-
1916 WILHELM BLASCHKE, Kreis und Kugel, Leipzig.
-
1916 WILHELM BLASCHKE, Kreis und Kugel, Leipzig.
-
-
-
-
7
-
-
33846582467
-
-
1917 HANS MOHRMANN, Die Minimalzahl der stationären Ebenen eines räumlichen Ovals, Sitz. Ber. Kgl. Bayerischen Akad. Wiss. Math. Phys. K1, 1-3.
-
1917 HANS MOHRMANN, Die Minimalzahl der stationären Ebenen eines räumlichen Ovals, Sitz. Ber. Kgl. Bayerischen Akad. Wiss. Math. Phys. K1, 1-3.
-
-
-
-
8
-
-
33846648010
-
-
1922 HELLMUTH KNESER, Neuer Beweis des Vierscheitelsatzes, Christian Huygens 2,315-318.
-
1922 HELLMUTH KNESER, Neuer Beweis des Vierscheitelsatzes, Christian Huygens 2,315-318.
-
-
-
-
9
-
-
33846618286
-
-
1928 W. SÜSS, Ein Vierscheitelsatzbein geschlossenen Raumkurven, Tohoku Math. J. 29, 359-362.
-
1928 W. SÜSS, Ein Vierscheitelsatzbein geschlossenen Raumkurven, Tohoku Math. J. 29, 359-362.
-
-
-
-
10
-
-
33846618772
-
-
1930 WILHELM BLASCHKE, Vorlesungen über die Differentialgeometrie I, 3. Aufl. Springer-Verlag, Berlin, see p. 31.
-
1930 WILHELM BLASCHKE, Vorlesungen über die Differentialgeometrie I, 3. Aufl. Springer-Verlag, Berlin, see p. 31.
-
-
-
-
11
-
-
34250960587
-
-
1931 S. MUKHOPADHYAYA, Extended minimum-number theorems of cyclic and sextactic points on a plane convex oval, Math. Zeit. 33, 648-662.
-
1931 S. MUKHOPADHYAYA, Extended minimum-number theorems of cyclic and sextactic points on a plane convex oval, Math. Zeit. 33, 648-662.
-
-
-
-
12
-
-
33846641721
-
-
1933 DAVID FOG, Über den Vierscheitelsatz und seine Verallgemeinerungen, Sitzungsberichte Preuss. Akad. Wiss. Phys.-Math. Kl., Berlin, 251-254.
-
1933 DAVID FOG, Über den Vierscheitelsatz und seine Verallgemeinerungen, Sitzungsberichte Preuss. Akad. Wiss. Phys.-Math. Kl., Berlin, 251-254.
-
-
-
-
13
-
-
34347188733
-
-
1933 OTTO HAUPT, Zur Theorie der Ordnung reeler Kurven in der Ebene bezüglich vorgegebener Kurvenscharen, Monatsh. Math. Phys.40, 1-53.
-
1933 OTTO HAUPT, Zur Theorie der Ordnung reeler Kurven in der Ebene bezüglich vorgegebener Kurvenscharen, Monatsh. Math. Phys.40, 1-53.
-
-
-
-
14
-
-
33846588906
-
-
1934 T. TAKASU, Vierscheitelsatz für Raumkurven, Tohoku Math. J. 39, 292-298.
-
1934 T. TAKASU, Vierscheitelsatz für Raumkurven, Tohoku Math. J. 39, 292-298.
-
-
-
-
15
-
-
84968502347
-
-
1937 W. C. GRAUSTEIN, Extensions of the four-vertex theorem, Trans. Amer. Math. Soc. 41, 9-23.
-
1937 W. C. GRAUSTEIN, Extensions of the four-vertex theorem, Trans. Amer. Math. Soc. 41, 9-23.
-
-
-
-
16
-
-
84966255043
-
-
1937 W. C. GRAUSTEIN and S. B. JACKSON, The fourvertex theoremfor a certain type of space curves, Bull. Amer. Math. Soc. 43,737-741.
-
1937 W. C. GRAUSTEIN and S. B. JACKSON, The fourvertex theoremfor a certain type of space curves, Bull. Amer. Math. Soc. 43,737-741.
-
-
-
-
17
-
-
33846642647
-
-
1940 S. B. JACKSON, The four-vertex theorem for spherical curves, Amer. J. Math. 62, 795-812.
-
1940 S. B. JACKSON, The four-vertex theorem for spherical curves, Amer. J. Math. 62, 795-812.
-
-
-
-
18
-
-
0041188685
-
Vertices of plane curves
-
_
-
1944 _, Vertices of plane curves, Bull. Amer. Math. Soc. 50, 564-578.
-
(1944)
Bull. Amer. Math. Soc
, vol.50
, pp. 564-578
-
-
-
19
-
-
33846606393
-
The four-vertex theorem for surfaces of constant curvature
-
_
-
1945 _, The four-vertex theorem for surfaces of constant curvature, Amer. J. Math. 67, 563-582.
-
(1945)
Amer. J. Math
, vol.67
, pp. 563-582
-
-
-
20
-
-
85009722941
-
PETER SCHERK, The four-vertex theorem
-
Montreal, Univ. of Toronto Press, Toronto
-
1946 PETER SCHERK, The four-vertex theorem, Proc. First Canadian Math. Congress, Montreal 1945, Univ. of Toronto Press, Toronto, 97-102.
-
(1945)
Proc. First Canadian Math. Congress
, pp. 97-102
-
-
-
21
-
-
22544479230
-
-
1952 L. VIETORIS, Ein einfacher Beweis des Vierscheitelsatzes der ebenen Kurven, Arch. Math. 3, 304-306.
-
1952 L. VIETORIS, Ein einfacher Beweis des Vierscheitelsatzes der ebenen Kurven, Arch. Math. 3, 304-306.
-
-
-
-
22
-
-
33846624731
-
-
1958 M. BARNER and F. FLOHR, Der Vierscheitelsatz und seine Verallgemeinerung, Der Mathematikunterricht 4, 43-73.
-
1958 M. BARNER and F. FLOHR, Der Vierscheitelsatz und seine Verallgemeinerung, Der Mathematikunterricht 4, 43-73.
-
-
-
-
23
-
-
33846601407
-
LESTER E. DUBINS, Another proof of the four vertex theorem
-
1960 LESTER E. DUBINS, Another proof of the four vertex theorem, Amer. Math. Monthly 67, 573-574.
-
(1960)
Amer. Math. Monthly
, vol.67
, pp. 573-574
-
-
-
24
-
-
33846642164
-
-
1961 DIRK STRUIK, Lectures on Classical Differential Geometry, 2nd ed., Addison-Wesley, Reading, MA, see p. 48.
-
1961 DIRK STRUIK, Lectures on Classical Differential Geometry, 2nd ed., Addison-Wesley, Reading, MA, see p. 48.
-
-
-
-
25
-
-
33846563031
-
-
1965 DETLEF LAUGWITZ, Differential and Riemannian Geometry, Academic Press, New York, see p. 201.
-
1965 DETLEF LAUGWITZ, Differential and Riemannian Geometry, Academic Press, New York, see p. 201.
-
-
-
-
26
-
-
33846576181
-
-
1967 SHIING-SHEN CHERN, Curves and surfaces in euclidean space, Studies in Global Geometry and Analysis, MAA Studies in Math. 4, Math. Assoc. of America, Washington, DC, 16-56.
-
1967 SHIING-SHEN CHERN, Curves and surfaces in euclidean space, Studies in Global Geometry and Analysis, MAA Studies in Math. 4, Math. Assoc. of America, Washington, DC, 16-56.
-
-
-
-
27
-
-
33846604681
-
-
1967 O. HAUPT and H. KÜNNETH, Geometrische Ordnung, Springer-Verlag, Berlin-Heidelberg-New York.
-
1967 O. HAUPT and H. KÜNNETH, Geometrische Ordnung, Springer-Verlag, Berlin-Heidelberg-New York.
-
-
-
-
28
-
-
22544453974
-
HERMAN GLUCK, The converse to the four-vertex theorem
-
1971 HERMAN GLUCK, The converse to the four-vertex theorem, L'Enseignement Math. 17, 295-309.
-
(1971)
L'Enseignement Math
, vol.17
, pp. 295-309
-
-
-
29
-
-
7544232475
-
The generalized Minkowski problem in differential geometry in the large
-
_
-
1972 _, The generalized Minkowski problem in differential geometry in the large, Ann. Math. 96, 245-276.
-
(1972)
Ann. Math
, vol.96
, pp. 245-276
-
-
-
30
-
-
33846624270
-
-
1972 MARCEL BERGER and BERNARD GOSTIAUX, Géométrie Différentielle, Armand Colin, Paris, seep. 362.
-
1972 MARCEL BERGER and BERNARD GOSTIAUX, Géométrie Différentielle, Armand Colin, Paris, seep. 362.
-
-
-
-
31
-
-
84968476144
-
HERMAN GLUCK, Manifolds with preassigned curvature - a survey
-
1975 HERMAN GLUCK, Manifolds with preassigned curvature - a survey, Bull. Amer. Math. Soc. 81, 313-329.
-
(1975)
Bull. Amer. Math. Soc
, vol.81
, pp. 313-329
-
-
-
32
-
-
33846569994
-
-
1976 MANFREDO DO CARMO, Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, NJ, see p. 37.
-
1976 MANFREDO DO CARMO, Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, NJ, see p. 37.
-
-
-
-
33
-
-
34250390216
-
GUDLAUGUR THORBERGSSON, Vierscheitelsatz auf Flächen nichtpositiver Krümmung
-
1976 GUDLAUGUR THORBERGSSON, Vierscheitelsatz auf Flächen nichtpositiver Krümmung, Math. Zeit. 149, No. 1, 47-56.
-
(1976)
Math. Zeit
, vol.149
, Issue.1
, pp. 47-56
-
-
-
34
-
-
33846633742
-
-
1978 WILHELM KLINGENBERG, A Course in Differential Geometry, Springer-Verlag, New York, see p. 28.
-
1978 WILHELM KLINGENBERG, A Course in Differential Geometry, Springer-Verlag, New York, see p. 28.
-
-
-
-
35
-
-
0005766376
-
ROBERT OSSERMAN, The Four-or-More Vertex Theorem
-
1985 ROBERT OSSERMAN, The Four-or-More Vertex Theorem, Amer. Math. Monthly 92, No. 5, 332-337.
-
(1985)
Amer. Math. Monthly
, vol.92
, Issue.5
, pp. 332-337
-
-
-
36
-
-
0039409198
-
ULRICH PINKALL, On the four-vertex theorem
-
1987 ULRICH PINKALL, On the four-vertex theorem, Aequationes Math. 34, No. 2-3, 221-230.
-
(1987)
Aequationes Math
, vol.34
, Issue.2-3
, pp. 221-230
-
-
-
37
-
-
3843134988
-
-
1992 GRANT CAIRNS, MEHMET Ö ZDEMIR, EKKEHARD H. TJADEN, A counterexample to a conjecture of U. Pinkall, Topology 31, No. 3, 557-558.
-
1992 GRANT CAIRNS, MEHMET Ö ZDEMIR, EKKEHARD H. TJADEN, A counterexample to a conjecture of U. Pinkall, Topology 31, No. 3, 557-558.
-
-
-
-
38
-
-
84963018584
-
-
1994 V. D. SEDYKH, Four vertices of a convex space curve, Bull. London Math. Soc. 26, No. 2, 177-180.
-
1994 V. D. SEDYKH, Four vertices of a convex space curve, Bull. London Math. Soc. 26, No. 2, 177-180.
-
-
-
-
39
-
-
84972505056
-
MASAAKI UMEHARA, 6-vertex theorem for closed planar curve which bounds an immersed surface with nonzero genus
-
1994 MASAAKI UMEHARA, 6-vertex theorem for closed planar curve which bounds an immersed surface with nonzero genus, Nagoya Math. J. 134, 75-89.
-
(1994)
Nagoya Math. J
, vol.134
, pp. 75-89
-
-
-
40
-
-
33846645454
-
-
1995 ÉTIENNE GHYS, Cercles osculateurs et géométrie lorentzienne, Talk at the journée inaugurale du CMI, Marseille.
-
1995 ÉTIENNE GHYS, Cercles osculateurs et géométrie lorentzienne, Talk at the journée inaugurale du CMI, Marseille.
-
-
-
-
41
-
-
0040749607
-
OSAMU KOBAYASHI and MASAAKI UMEHARA, Geometry of Scrolls
-
1996 OSAMU KOBAYASHI and MASAAKI UMEHARA, Geometry of Scrolls, Osaka J. Math. 33, 441-473.
-
(1996)
Osaka J. Math
, vol.33
, pp. 441-473
-
-
-
42
-
-
33846566859
-
-
1998 MASAO MAEDA, The four-or-more vertex theorems in 2-dimensional space forms, Nat. Sci. 3, Fac. Educ. Hum. Sci. Yokohama Natl. Univ. No. 1, 43-46.
-
1998 MASAO MAEDA, The four-or-more vertex theorems in 2-dimensional space forms, Nat. Sci. 3, Fac. Educ. Hum. Sci. Yokohama Natl. Univ. No. 1, 43-46.
-
-
-
-
43
-
-
0011575140
-
MASAAKI UMEHARA, A unified approach to the four vertex theorems I, Differential and Symplectic Topology of Knots and Curves
-
1999 MASAAKI UMEHARA, A unified approach to the four vertex theorems I, Differential and Symplectic Topology of Knots and Curves, Amer. Math. Soc. Translations, Ser. 2, Vol 190, 185-228.
-
(1999)
Amer. Math. Soc. Translations, Ser. 2
, vol.190
, pp. 185-228
-
-
-
44
-
-
33846608710
-
-
1999 GUDLAUGUR THORBERGSSON and MASAAKI UMEHARA, A unified approach to the four vertex theorems II, Differential and Symplectic Topology of Knots and Curves, Amer. Math. Soc. Translations, Ser. 2, 190, 229-252.
-
1999 GUDLAUGUR THORBERGSSON and MASAAKI UMEHARA, A unified approach to the four vertex theorems II, Differential and Symplectic Topology of Knots and Curves, Amer. Math. Soc. Translations, Ser. 2, Vol 190, 229-252.
-
-
-
-
45
-
-
33846602307
-
-
2000 S. I. R. COSTA and M. FIRER, Four-or-more vertex theorems for constant curvature manifolds, Real and complex singularities (São Carlos, 1998) Res. Notes Math., 412, Chapman and Hall/CRC, Boca Raton, FL, 164-172.
-
2000 S. I. R. COSTA and M. FIRER, Four-or-more vertex theorems for constant curvature manifolds, Real and complex singularities (São Carlos, 1998) Res. Notes Math., 412, Chapman and Hall/CRC, Boca Raton, FL, 164-172.
-
-
-
-
46
-
-
85009826585
-
DAVID SINGER, Diffeomorphisms of the circle and hyperbolic curvature
-
2001 DAVID SINGER, Diffeomorphisms of the circle and hyperbolic curvature, Conformal Geometry and Dynamics 5, 1-5.
-
(2001)
Conformal Geometry and Dynamics
, vol.5
, pp. 1-5
-
-
-
47
-
-
33846606879
-
-
2004 V. OVSIENKO and S. TABACHNIKOV, Projective differential geometry old and new: from Schwarzian derivative to cohomology of diffeomorphism groups, Cambridge Tracts in Mathematics 165, Cambridge University Press.
-
2004 V. OVSIENKO and S. TABACHNIKOV, Projective differential geometry old and new: from Schwarzian derivative to cohomology of diffeomorphism groups, Cambridge Tracts in Mathematics 165, Cambridge University Press.
-
-
-
-
48
-
-
22544432533
-
BJÖRN DAHLBERG, The Converse of the Four Vertex Theorem, (edited posthumously by Vilhelm Adolf sson and Peter Kumlin)
-
2005 BJÖRN DAHLBERG, The Converse of the Four Vertex Theorem, (edited posthumously by Vilhelm Adolf sson and Peter Kumlin), Proc. Amer. Math. Soc. 133, 2131-2135.
-
(2005)
Proc. Amer. Math. Soc
, vol.133
, pp. 2131-2135
-
-
|