Differentiability of quermassintegrals: A classification of convex bodies

DOI10.1090/S0002-9947-2013-05723-6zbMath1296.52002OpenAlexW1966476655MaRDI QIDQ5402102

María A. Hernández Cifre, E. Saorín

Publication date: 5 March 2014

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: http://www.ams.org/journals/tran/2014-366-02/S0002-9947-2013-05723-6

zbMATH Keywords

tangential bodyextreme vectorform bodyinner parallel bodycap bodySteiner polynomialTeissier problemHadwiger classification

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (4)

On the roots of polynomials with log-convex coefficients ⋮ On characterizations of sausages via inequalities and roots of Steiner polynomials ⋮ On the monotonicity of the isoperimetric quotient for parallel bodies ⋮ A new counterexample to Sangwine-Yager's conjecture

Cites Work

• On inner parallel bodies and quermassintegrals
• Notes on the roots of Steiner polynomials
• Some inequalities about mixed volumes
• On the location of roots of Steiner polynomials
• Beweis einer Vermutung von H. Minkowski
• Über eine neue isoperimetrische Ungleichung für konvexe Polyeder
• On the volume of inner parallel bodies
• Bonnesen-Style Inequalities for Minkowski Relative Geometry
• La formule de Steiner pour les érosions
• On the roots of the Steiner polynomial of a 3-dimensional convex body
• On differentiability of quermassintegrals
• Convex and Discrete Geometry
• Bemerkung zu einer Verschärfung der isoperimetrischen Ungleichung durch H. Hadwiger
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