Abstract.
We give a necessary condition for a convex body in \( \Bbb R^n \) to have minimal volume in the class of all convex sets with prescribed constant brightness.¶Such a condition permits us to prove that in the class of all convex bodies of revolution with given constant brightness the unique element of minimal volume is a body described by Blaschke as an example of a non-spherical solid of constant brightness.
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Received: 9.12.1996; final version received 5.9.1997.
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Gronchi, P. Bodies of constant brightness. Arch. Math. 70, 489–498 (1998). https://doi.org/10.1007/s000130050224
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DOI: https://doi.org/10.1007/s000130050224