Among others, we prove that if a convex body K and a ball B have equal constant volumes of caps and equal constant areas of sections with respect to the supporting planes of a sphere, then K≡B
Abstract. For a convex body of given volume in spherical space, the total invariant measure of hitti...
Barker and Larman asked the following. Let K′⊂ Rd be a convex body, whose interior contains a given ...
We initiate a systematic investigation into the nature of the function ∝K(L,ρ) that gives the volume...
AbstractSuppose that K and L are convex bodies in Rn with L⊂intK. For each hyperplane H⊂Rn which sup...
A celebrated theorem of P. Funk, 1916, states that an origin-centered star body in R3 is determined ...
A celebrated theorem of P. Funk, 1916, states that an origin-centered star body in R3 is determined ...
Several affirmative answers are given in any dimension for Ulam's question about bodies floating sta...
In this note, we prove the following inequality for the norm of a convex body $K$ in $\mathbb{R}^n$,...
AbstractIn this paper, we discuss the determination of a convex or star-shaped body K in Rd by infor...
AbstractNew definitions of a star body and its radial function are given. These are used in studying...
Abstract. Let Ω be a domain in the N-dimensional Euclidean space and let Γ be an open portion of its...
AbstractIn 1926 Nakajima (= Matsumura) showed that any convex body in R3 with constant width, consta...
AbstractNew definitions of a star body and its radial function are given. These are used in studying...
In (1) Dvoretsky proved, using very ingenious methods, that every centrally symmetric convex body of...
High proved the following theorem. If the intersections of any two congruent copies of a plane conve...
Abstract. For a convex body of given volume in spherical space, the total invariant measure of hitti...
Barker and Larman asked the following. Let K′⊂ Rd be a convex body, whose interior contains a given ...
We initiate a systematic investigation into the nature of the function ∝K(L,ρ) that gives the volume...
AbstractSuppose that K and L are convex bodies in Rn with L⊂intK. For each hyperplane H⊂Rn which sup...
A celebrated theorem of P. Funk, 1916, states that an origin-centered star body in R3 is determined ...
A celebrated theorem of P. Funk, 1916, states that an origin-centered star body in R3 is determined ...
Several affirmative answers are given in any dimension for Ulam's question about bodies floating sta...
In this note, we prove the following inequality for the norm of a convex body $K$ in $\mathbb{R}^n$,...
AbstractIn this paper, we discuss the determination of a convex or star-shaped body K in Rd by infor...
AbstractNew definitions of a star body and its radial function are given. These are used in studying...
Abstract. Let Ω be a domain in the N-dimensional Euclidean space and let Γ be an open portion of its...
AbstractIn 1926 Nakajima (= Matsumura) showed that any convex body in R3 with constant width, consta...
AbstractNew definitions of a star body and its radial function are given. These are used in studying...
In (1) Dvoretsky proved, using very ingenious methods, that every centrally symmetric convex body of...
High proved the following theorem. If the intersections of any two congruent copies of a plane conve...
Abstract. For a convex body of given volume in spherical space, the total invariant measure of hitti...
Barker and Larman asked the following. Let K′⊂ Rd be a convex body, whose interior contains a given ...
We initiate a systematic investigation into the nature of the function ∝K(L,ρ) that gives the volume...
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