On Perimeters and Volumes of Fattened Sets

Andrea C. G. Mennucci

International Journal of Mathematics and Mathematical Sciences, 2019, vol. 2019, 1-12

Abstract:

In this paper we analyze the shape of fattened sets; given a compact set let be its fattened set; we prove a general bound between the perimeter of and the Lebesgue measure of . We provide two proofs: one elementary and one based on Geometric Measure Theory. Note that, by the Flemin–Rishel coarea formula, is integrable for . We further show that for any integrable continuous decreasing function there exists a compact set such that . These results solve a conjecture left open in (Mennucci and Duci, 2015) and provide new insight in applications where the fattened set plays an important role.

Date: 2019
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2019/8283496.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2019/8283496.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:8283496

DOI: 10.1155/2019/8283496

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().