On a Brunn-Minkowski theorem for a geometric domain functional considered by Avhadiev.
On a Differential Inequality and Its Applications to Geometry.
On a discrete Dido-type question.
On a geometric inequality by J. Sándor.
On a problem by Shapiro.
On a question of Milman and Alesker concerning the monotonicity of a domain functional.
On area and side lengths of triangles in normed planes
Let be a d-dimensional normed space with norm ||·|| and let B be the unit ball in . Let us fix a Lebesgue measure in with . This measure will play the role of the volume in . We consider an arbitrary simplex T in with prescribed edge lengths. For the case d = 2, sharp upper and lower bounds of are determined. For d ≥ 3 it is noticed that the tight lower bound of is zero.
On billiard arcs
On Busemann surface area of the unit ball in Minkowski spaces.
On extremal solutions of martingale problems
On Gaussian Brunn-Minkowski inequalities
We are interested in Gaussian versions of the classical Brunn-Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrhard inequality for m Borel or convex sets based on a previous work by Borell. Our method also yields semigroup proofs of the geometric Brascamp-Lieb inequality and of its reverse form, which follow exactly the same lines.
On Hadwiger's problem on inner parallel bodies
We consider the problem of classifying the convex bodies in the 3-dimensional space depending on the differentiability of their associated quermassintegrals with respect to the one-parameter-depending family given by the inner/outer parallel bodies. It turns out that this problem is closely related to some behavior of the roots of the 3-dimensional Steiner polynomial.
On isoperimetric inequalities in Minkowski spaces.
On linked Jordan curves in
On minimum area quadrilaterals and triangles circumscribed about convex plane regions.
On new isoperimetric inequalities and symmetrization.
On non-inscribable polytopes
On optimal route planning evading cubes in the three space.
On periodic homeomorphisms of spheres.
On Reuleaux triangles in Minkowski planes.