Generalization of projection constants: sufficient enlargements.
Geometry of finite-dimensional normed spaces and continuous functions on the Euclidean sphere.
Hypercontractivity and comparison of moments of iterated maxima and minima of independent random variables.
Hyperplane conjecture for quotient spaces of Lp.
-measures in Minkowski planes.
Inequalities for Convex Bodies and Polar Reciprocal Lattices in Rn.
Isometric classification of Sobolev spaces on graphs
Isometric Sobolev spaces on finite graphs are characterized. The characterization implies that the following analogue of the Banach-Stone theorem is valid: if two Sobolev spaces on 3-connected graphs, with the exponent which is not an even integer, are isometric, then the corresponding graphs are isomorphic. As a corollary it is shown that for each finite group and each p which is not an even integer, there exists n ∈ ℕ and a subspace whose group of isometries is the direct product × ℤ₂.
Large equilateral triangles inscribed in the unit disk of a Minkowski plane.
Minimal surfaces shells containing a convex surface in Minkowski space.
Minimum Steiner Trees in Normed Planes.
Monotonicity of the maximum of inner product norms
Let be the field of real or complex numbers. In this note we characterize all inner product norms on for which the norm on is monotonic.
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 areas and integral geometry in Minkowski spaces.
On Asymptotic Volume of Tori.
On boundary arcs joining antipodal points of a planar convex body.
On Busemann surface area of the unit ball in Minkowski spaces.
On cross-section measures in Minkowski spaces.
On isoperimetric inequalities in Minkowski spaces.
On shadow boundaries of centrally symmetric convex bodies.
On the Busemann area in Minkowski spaces.