Add to ORKGA theorem due to Favard states that among all plane sets of given area and perimeter, the symmetric lens has maximum circumradius. This paper deals with the higher dimensional problem of finding the convex body in R3 of given volume and mean width with the largest possible diameter. It is shown that the solution is the convex hull of a surface of revolution with constant Gauss curvature and a segment lying on the axis of revolution. Such a body is conjectured to maximize also the circumradius in the same class. 1
Curvature measure is one of the basic notion in the theory of convex bodies. Together with surface a...
Abstract. We initiate a systematic investigation into the nature of the function αK(L, ρ) that gives...
Abstract. We initiate a systematic investigation into the nature of the function a(K; L; r) that giv...
A theorem due to Favard states that among all plane sets of given area and perimeter, the symmetric ...
Abstract. A theorem due to Favard states that among all plane sets of given area and perimeter, the ...
A well-known result in convex geometry proved by Favard states that among all convex plane sets of g...
If K is a convex body in the Euclidean space En, we consider the six classic geometric functionals a...
International audienceIt is shown that the cross-section body of a convex body K subset of R-3, that...
A translation body of a convex body is the convex hull of two of its translates intersecting each ot...
Abstract. We show that in all dimensions d ≥ 3, there exists an asymmetric convex body of revolution...
We propose developing new tools and approaches towards resolving the conjecture posed in [KLS95], wh...
Consider a compact convex set C in the 3-dimensional space R3, of constant thickness l> 0, that i...
It is shown that if C is an /j-dimensional convex body then there is an affine image C of C for whic...
Abstract. A translation body of a convex body is the convex hull of two of its translates intersecti...
In this work we study the fencing problem consisting of finding a trisection of a 3-rotationally sy...
Curvature measure is one of the basic notion in the theory of convex bodies. Together with surface a...
Abstract. We initiate a systematic investigation into the nature of the function αK(L, ρ) that gives...
Abstract. We initiate a systematic investigation into the nature of the function a(K; L; r) that giv...
A theorem due to Favard states that among all plane sets of given area and perimeter, the symmetric ...
Abstract. A theorem due to Favard states that among all plane sets of given area and perimeter, the ...
A well-known result in convex geometry proved by Favard states that among all convex plane sets of g...
If K is a convex body in the Euclidean space En, we consider the six classic geometric functionals a...
International audienceIt is shown that the cross-section body of a convex body K subset of R-3, that...
A translation body of a convex body is the convex hull of two of its translates intersecting each ot...
Abstract. We show that in all dimensions d ≥ 3, there exists an asymmetric convex body of revolution...
We propose developing new tools and approaches towards resolving the conjecture posed in [KLS95], wh...
Consider a compact convex set C in the 3-dimensional space R3, of constant thickness l> 0, that i...
It is shown that if C is an /j-dimensional convex body then there is an affine image C of C for whic...
Abstract. A translation body of a convex body is the convex hull of two of its translates intersecti...
In this work we study the fencing problem consisting of finding a trisection of a 3-rotationally sy...
Curvature measure is one of the basic notion in the theory of convex bodies. Together with surface a...
Abstract. We initiate a systematic investigation into the nature of the function αK(L, ρ) that gives...
Abstract. We initiate a systematic investigation into the nature of the function a(K; L; r) that giv...