On the isodiametric and isominwidth inequalities for planar bisections
For a given planar convex body K, a bisection of K is a decomposition of K into two closed sets A,B so that A∩B is an injective continuous curve connecting exactly two boundary points of K. Consider a bisection of K minimizing, over all bisections, the maximum diameter (resp., maximum width) of the...
| Authors: | ; |
|---|---|
| Format: | Article |
| Status: | Published version |
| Publication date: | 2021 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/134619 |
| Online Access: | https://hdl.handle.net/11441/134619 https://doi.org/10.4171/rmi/1225 |
| Access Level: | Open access |
| Keyword: | Planar convex bodies Maximum bisecting diameter Maximum bisecting width Minimizing bisections |
| _version_ | 1878742748664692736 |
|---|---|
| author | Cañete Martín, Antonio Jesús |
| author2 | González Merino, Bernardo |
| author2_role | author |
| author_browse | Cañete Martín, Antonio Jesús González Merino, Bernardo |
| author_facet | Cañete Martín, Antonio Jesús González Merino, Bernardo |
| author_role | author |
| collection | idUS. Depósito de Investigación de la Universidad de Sevilla |
| description | For a given planar convex body K, a bisection of K is a decomposition of K into two closed sets A,B so that A∩B is an injective continuous curve connecting exactly two boundary points of K. Consider a bisection of K minimizing, over all bisections, the maximum diameter (resp., maximum width) of the sets in the decomposition. In this note, we study some properties of these minimizing bisections and prove inequalities extending the classical isodiametric and isominwidth inequalities. Furthermore, we address the corresponding reverse optimization problems and establish inequalities similar to the reverse isodiametric and reverse isominwidth inequalities. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_fb8a0ec79afa79cf04adfac53c5218f2 |
| institution | Universidad de Sevilla (US) |
| instname_str | Universidad de Sevilla (US) |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:idus.us.es:11441/134619 |
| publishDate | 2021 |
| publishDateSort | 2021 |
| publisher | European Mathematical Society (EMS) |
| publisherStr | European Mathematical Society (EMS) |
| reponame_str | idUS. Depósito de Investigación de la Universidad de Sevilla |
| spelling | On the isodiametric and isominwidth inequalities for planar bisections Cañete Martín, Antonio Jesús González Merino, Bernardo Planar convex bodies Maximum bisecting diameter Maximum bisecting width Minimizing bisections For a given planar convex body K, a bisection of K is a decomposition of K into two closed sets A,B so that A∩B is an injective continuous curve connecting exactly two boundary points of K. Consider a bisection of K minimizing, over all bisections, the maximum diameter (resp., maximum width) of the sets in the decomposition. In this note, we study some properties of these minimizing bisections and prove inequalities extending the classical isodiametric and isominwidth inequalities. Furthermore, we address the corresponding reverse optimization problems and establish inequalities similar to the reverse isodiametric and reverse isominwidth inequalities. Ministerio de Ciencia, Innovación y Universidades MTM2017-84851-C2-1-P Junta de Andalucía FQM-325 Fundación Séneca 19901/GERM/15 Ministerio de Ciencia, Innovación y Universidades PGC2018-094215-B-I00 European Mathematical Society (EMS) https://hdl.handle.net/11441/134619 https://doi.org/10.4171/rmi/1225 |
| spellingShingle | On the isodiametric and isominwidth inequalities for planar bisections Cañete Martín, Antonio Jesús Planar convex bodies Maximum bisecting diameter Maximum bisecting width Minimizing bisections |
| status_str | publishedVersion |
| title | On the isodiametric and isominwidth inequalities for planar bisections |
| title_full | On the isodiametric and isominwidth inequalities for planar bisections |
| title_fullStr | On the isodiametric and isominwidth inequalities for planar bisections |
| title_full_unstemmed | On the isodiametric and isominwidth inequalities for planar bisections |
| title_short | On the isodiametric and isominwidth inequalities for planar bisections |
| title_sort | On the isodiametric and isominwidth inequalities for planar bisections |
| topic | Planar convex bodies Maximum bisecting diameter Maximum bisecting width Minimizing bisections |
| topic_facet | Planar convex bodies Maximum bisecting diameter Maximum bisecting width Minimizing bisections |
| url | https://hdl.handle.net/11441/134619 https://doi.org/10.4171/rmi/1225 |