Characterizations of balls by sections and caps. (English) Zbl 1330.52013
The main result of this paper shows that if a convex body and a ball have equal constant volume of caps and equal constant areas of sections with respect to the supporting planes of a sphere, then the convex body is identical to the ball.
Reviewer: Guangxian Zhu (New York)
MSC:
| 52A40 | Inequalities and extremum problems involving convexity in convex geometry |
| 52A38 | Length, area, volume and convex sets (aspects of convex geometry) |
References:
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