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References
SHOWING 1-10 OF 744 REFERENCES
n-dimensional area and content in Minkowski spaces
- Mathematics
- 1979
A definition of content in Minkowski spaces (of any finite dimension) is given which implies that the surface of the unit ball and that of the dual ball are equal. Various consequences of this…
The volume of convex bodies and Banach space geometry
- Mathematics
- 1989
Introduction 1. Notation and preliminary background 2. Gaussian variables. K-convexity 3. Ellipsoids 4. Dvoretzky's theorem 5. Entropy, approximation numbers, and Gaussian processes 6. Volume ratio…
On closed curves in Minkowski spaces
- Mathematics
- 1972
This note answers some of the questions raised by H. Herda in [1]. Let M be a Minkowski (finite dimensional real Banach) space with unit ball B. Let y be a simple closed rectifiable curve in M. For x…
Cardinalities of k-distance sets in Minkowski spaces
- MathematicsDiscret. Math.
- 1999
This work conjecture that a k-distance set in a d-dimensional Banach space, contains at most (k + 1) points, is solved in the affirmative for all 2-dimensional spaces and for spaces where the unit ball is a parallelotope.
On Bisectors in Minkowski Normed Spaces
- Mathematics
- 2000
We discuss the concept of the bisector of a segment in a Minkowski normed n-space, and prove that if the unit ball K of the space is strictly convex then all bisectors are topological images of a…
On the self-length of two-dimensional Banach spaces
- MathematicsBulletin of the Australian Mathematical Society
- 1996
The aim of this paper is to prove the following result: if X is a 2-dimensional symmetric real Banach space, then its self-length is greater than or equal to 2π. Moreover, the minimum value 2π is…
Geometry of Banach Spaces: Selected Topics
- Mathematics
- 1975
Support functionals for closed bounded convex subsets of a Banach space.- Convexity and differentiability of norms.- Uniformly convex and uniformly smooth Banach spaces.- The classical renorming…
On the level sets of a distance function in a Minkowski space
- Mathematics
- 1972
Given a closed subset of an n-dimensional Minkowski space with a strictly convex or differentiable norm, then, for almost every r > 0, the r-level set (points whose distance from the closed set is r)…
Excursions into Combinatorial Geometry
- Mathematics
- 1996
The book deals with the combinatorial geometry of convex bodies in finite-dimensional spaces. A general introduction to geometric convexity is followed by the investigation of d-convexity and…