Blaschke's Theorem Research Articles

Notes on Computable Analysis

Computable analysis has been part of computability theory since Turing's original paper on the subject (Turing, Proc. London Math. Sc. 42:230---265, 1936). Nevertheless, it is difficult to locate basic results in this area. A first goal of this paper is to give some new simple proofs of fundamental classical results (highlighting the role of ź10${{\Pi }_{1}^{0}}$ classes). Naturally this paper cannot cover all aspects of computable analysis, but we hope that this gives the reader a completely self-contained ingress into this area. A second goal is to use tools from effective topology to analyse the Darboux property, particularly a result by Sierpinski, and the Blaschke Selection Theorem.

Extension of bounded vector‐valued functions

AbstractIn this paper we consider extensions of bounded vector‐valued holomorphic (or harmonic or pluriharmonic) functions defined on subsets of an open set Ω ⊂ ℝN. The results are based on the description of vector‐valued functions as operators. As an application we prove a vector‐valued version of Blaschke's theorem (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On the lattice diameter of a convex polygon

The lattice diameter, ℓ(P), of a convex polygon P in R 2 measures the longest string of integer points on a line contained in P. We relate the lattice diameter to the area and to the lattice width of P, w l(P) . We show, e.g., that w l⩽ 4 3 ℓ+1 , thus giving a discrete analogue of Blaschke's theorem.

Blaschke's theorem for convex hypersurfaces

Blaschke's theorem for convex hypersurfaces

Analytic proof of Blaschke's theorem on the curve of constant breadth, II

Analytic proof of Blaschke's theorem on the curve of constant breadth, II

Analytic proof of Blaschke's theorem on the curve of constant breadth with minimum area

Analytic proof of Blaschke's theorem on the curve of constant breadth with minimum area