The Willmore functional and the containment problem in \(R^{4}\)

DOI10.1007/s11425-007-0029-0zbMath1118.52010OpenAlexW2137471064WikidataQ125690515 ScholiaQ125690515MaRDI QIDQ885566

Jia-zu Zhou

Publication date: 14 June 2007

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-007-0029-0

zbMATH Keywords

scalar curvaturemean curvatureconvex bodyWillmore functionalkinematic formulaconvex hypersurfaceHadwiger's conditionHadwiger's containment problemMinkowski quermassintegrals

Mathematics Subject Classification ID

Integral geometry (53C65) Convex sets in (3) dimensions (including convex surfaces) (52A15) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

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Kinematic formulas of total mean curvatures for hypersurfaces ⋮ Reverse Bonnesen-style inequalities on surfaces of constant curvature ⋮ Reverse Bonnesen style inequalities in a surface \(\mathbb{X}_\epsilon ^2\) of constant curvature ⋮ An isoperimetric deficit upper bound of the convex domain in a surface of constant curvature ⋮ Some Bonnesen-style inequalities for higher dimensions ⋮ On containment measure and the mixed isoperimetric inequality ⋮ A kinematic formula for integral invariant of degree 4 in real space form

Cites Work

• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• A sufficient condition for one convex body containing another
• Überdeckung ebener Bereiche durch Kreise und Quadrate
• Sufficient conditions for one domain to contain another in a space of constant curvature
• The kinematic formula in Riemannian homogeneous spaces
• Geometric inequalities and inclusion measures of convex bodies
• The Sufficient Condition for a Convex Body to Enclose Another in ℝ 4
• Kinematic Formulas for Mean Curvature Powers of Hypersurfaces and Hadwiger's Theorem in ℝ 2n
• On the Kinematic Formula in the Euclidean Space of N Dimensions
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