×

Integral inequalities for ovaloids in Euclidean space. (English) Zbl 0627.53002

For smooth ovaloids in Euclidean space \(E^ 3\), the authors derive integral inequalities involving, besides the Gauss curvature, traces of powers of the Weingarten map and their Beltrami operators with respect to the second fundamental form. Some known characterizations of the sphere are obtained as corollaries.
Reviewer: R.Schneider

MSC:

53A05 Surfaces in Euclidean and related spaces
53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1216/RMJ-1975-5-1-135 · Zbl 0303.53018 · doi:10.1216/RMJ-1975-5-1-135
[2] DOI: 10.1007/BF01173099 · Zbl 0172.46701 · doi:10.1007/BF01173099
[3] DOI: 10.2307/2032934 · Zbl 0067.13801 · doi:10.2307/2032934
[4] Hasanis, Colloquium Math 48 pp 49– (1984)
[5] DOI: 10.2307/2038475 · Zbl 0222.53047 · doi:10.2307/2038475
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.