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A Blaschke–Lebesgue theorem for the Cheeger constant.
- Source :
-
Communications in Contemporary Mathematics . May2024, Vol. 26 Issue 4, p1-41. 41p. - Publication Year :
- 2024
-
Abstract
- In this paper, we prove a new extremal property of the Reuleaux triangle: it maximizes the Cheeger constant among all bodies of (same) constant width. The proof relies on a fine analysis of the optimality conditions satisfied by an optimal Reuleaux polygon together with an explicit upper bound for the inradius of the optimal domain. As a possible perspective, we conjecture that this maximal property of the Reuleaux triangle holds for the first eigenvalue of the p -Laplacian for any p ∈ (1 , + ∞) (this paper covers the case p = 1 whereas the case p = + ∞ was already known). [ABSTRACT FROM AUTHOR]
- Subjects :
- *POLYGONS
*TRIANGLES
*EIGENVALUES
*LOGICAL prediction
Subjects
Details
- Language :
- English
- ISSN :
- 02191997
- Volume :
- 26
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Communications in Contemporary Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 176558090
- Full Text :
- https://doi.org/10.1142/S0219199723500244