We carry out an analysis of the size of the contact surface between a Cheeger set E and its ambient space Omega subset of R-d. By providing bounds on the Hausdorff dimension of the contact surface partial derivative E boolean AND partial derivative Omega, we show a fruitful interplay between this size itself and the regularity of the boundaries. Eventually, we obtain sufficient conditions to infer that the contact surface has positive (d -1) dimensional Hausdorff measure. Finally we prove by explicit examples in two dimensions that such bounds are optimal. (C) 2021 Elsevier Masson SAS. All rights reserved.
Dimensional lower bounds for contact surfaces of Cheeger sets / Caroccia, M; Ciani, S. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - ELETTRONICO. - 157:(2022), pp. 1-44. [10.1016/j.matpur.2021.11.010]
Dimensional lower bounds for contact surfaces of Cheeger sets
Ciani, S
2022
Abstract
We carry out an analysis of the size of the contact surface between a Cheeger set E and its ambient space Omega subset of R-d. By providing bounds on the Hausdorff dimension of the contact surface partial derivative E boolean AND partial derivative Omega, we show a fruitful interplay between this size itself and the regularity of the boundaries. Eventually, we obtain sufficient conditions to infer that the contact surface has positive (d -1) dimensional Hausdorff measure. Finally we prove by explicit examples in two dimensions that such bounds are optimal. (C) 2021 Elsevier Masson SAS. All rights reserved.| File | Dimensione | Formato | |
|---|---|---|---|
|
2005.06439.pdf
Open Access dal 13/12/2023
Tipo:
Versione (PDF) editoriale
Licenza:
Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
Dimensione
1.16 MB
Formato
Adobe PDF
|
1.16 MB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
