Convexity theorem for isoparametric submanifolds

1986 ◽  
Vol 85 (3) ◽  
pp. 487-492 ◽  
Author(s):  
Chuu-Lian Terng
Keyword(s):  
Convexity Theorem ◽  
Isoparametric Submanifolds

A New Proof of an Inequality of Heinz

1964 ◽  
Vol 7 (1) ◽  
pp. 97-100
Author(s):  
P. S. Bullen
Keyword(s):  
Convexity Theorem ◽  
Heinz Inequality ◽  
Measure Spaces

In a recent paper, [l], Dixmier has proved Heinz' inequality by deducing it from a lemma due to Thorin. In this note it is proved directly from a convexity theorem.Let(M(k), ℳ(k), μ(k)), k = 0, …, n, be measure spaces and Lq(k) (M(k), ℳ(k), μ(k)) be all the functions on M(k) such that

scholarly journals Properties of the trajectories of set-valued integrals in banach spaces

1990 ◽  
Vol 41 (2) ◽  
pp. 271-281
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Separable Banach Space ◽  
Hausdorff Metric ◽  
Density Theorem ◽  
Mosco Convergence ◽  
Convexity Theorem ◽  
Convergence Theorems ◽  
Convergence Of Sets ◽  
Differentiability Properties

Let F: T → 2x \ {} be a closed-valued multifunction into a separable Banach space X. We define the sets and We prove various convergence theorems for those two sets using the Hausdorff metric and the Kuratowski-Mosco convergence of sets. Then we prove a density theorem of CF and a corresponding convexity theorem for F(·). Finally we study the “differentiability” properties of K(·). Our work extends and improves earlier ones by Artstein, Bridgland, Hermes and Papageorgiou.

Minimal isoparametric submanifolds of S7 and octonionic eigenmaps

2019 ◽  
Vol 63 ◽  
pp. 137-144
Author(s):  
Daniel F. Bustos ◽  
Jaime B. Ripoll ◽  
Fidelis Bittencourt ◽  
Edson S. Figueiredo ◽  
Pedro Fusieger
Keyword(s):  
Isoparametric Submanifolds
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