On a Carathéodory's conjecture on umbilics: representing ovaloids

zbMath0897.53003MaRDI QIDQ1378845

J. Ning

Publication date: 20 October 1998

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=RSMUP_1997__98__213_0

zbMATH Keywords

umbilicsstereographic projectionsupport functionCarathéodory's conjecturecurvature linesBonnet chartrepresentations of ovaloids

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Convex sets in (3) dimensions (including convex surfaces) (52A15) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45)

Related Items (2)

Normal curvatures of asymptotically constant graphs and Carathéodory’s conjecture ⋮ Ovaloids of \(\mathbb{R}^3\) and their umbilics: A differential equation approach

Cites Work

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• Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern.
• A proof of a conjecture of Loewner and of the conjecture of Caratheodory on umbilic points
• Über Nabelpunkte auf einer Eifläche
• On G. Bol's proof of Carathéodory's conjecture
• Seminar on Differential Geometry. (AM-102)
• On a Conjecture of Carathéodoryr Analyticity Versus Smoothness
• The determination of convex bodies from their mean radius of curvature functions
• The Weyl and Minkowski problems in differential geometry in the large

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