We prove a lower bound on the number of the convex components of a compact set with non-empty interior in Double-struck capital R-n for all n >= 2 . Our result generalizes and improves the inequalities previously obtained in [M. Carozza, F. Giannetti, F. Leonetti and A. Passarelli di Napoli, Convex components, Commun. Contemp. Math. 21 (2019), no.6, Article ID 1850036] and [M. La Civita and F. Leonetti, Convex components of a set and the measure of its boundary, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 56 2008/09, 71-78].
On the convex components of a set in ℝn / Giannetti, Flavia; Stefani, Giorgio. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - 35:1(2023), pp. 187-199. [10.1515/forum-2022-0203]
On the convex components of a set in ℝn
Stefani, Giorgio
2023-01-01
Abstract
We prove a lower bound on the number of the convex components of a compact set with non-empty interior in Double-struck capital R-n for all n >= 2 . Our result generalizes and improves the inequalities previously obtained in [M. Carozza, F. Giannetti, F. Leonetti and A. Passarelli di Napoli, Convex components, Commun. Contemp. Math. 21 (2019), no.6, Article ID 1850036] and [M. La Civita and F. Leonetti, Convex components of a set and the measure of its boundary, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 56 2008/09, 71-78].| File | Dimensione | Formato | |
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