Geodesic
Stability Theorems for Convex Domains of Constant Width
Canadian mathematical bulletin, Tome 31 (1988) no. 3, pp. 328-337

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It is known that among all plane convex domains of given constant width Reuleaux triangles have minimal and circular discs have maximal area. Some estimates are given concerning the following associated stability problem: If K is a convex domain of constant width w and if the area of K differs at most ∊ from the area of a Reuleaux triangle or a circular disc of width w, how close (in terms of the Hausdorff distance) is K to a Reuleaux triangle or a circular disc? Another result concerns the deviation of a convex domain M of diameter d from a convex domain of constant width if the perimeter of M is close to πd.
DOI : 10.4153/CMB-1988-048-3
Mots-clés : 52A10 
Groemer, H. Stability Theorems for Convex Domains of Constant Width. Canadian mathematical bulletin, Tome 31 (1988) no. 3, pp. 328-337. doi: 10.4153/CMB-1988-048-3
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     author = {Groemer, H.},
     title = {Stability {Theorems} for {Convex} {Domains} of {Constant} {Width}},
     journal = {Canadian mathematical bulletin},
     pages = {328--337},
     year = {1988},
     volume = {31},
     number = {3},
     doi = {10.4153/CMB-1988-048-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-048-3/}
}
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