1. Basic convexity 2. Boundary structure 3. Minkowski addition 4. Curvature measure and quermass integrals 5. Mixed volumes 6. Inequalities for mixed volumes 7. Selected applications Appendix.

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Convex bodies : the Brunn-Minkowski theory

Convex bodies: the brunn–minkowski theory

Computational geometry

Distance-Regular Graphs

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http://carmenere.ucsd.edu/pdfs/DCRN-BulloCortesMartinez-bibliography.pdf

Distributed Control of Robotic Networks

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 H-convexity, and by various applications. Recent research is discussed, for example the three (generally unsolved) problems from the combinatorial geometry of convex bodies: the Szoekefalvi-Nagy problem, the Borsuk problem, the Hadwiger covering problem. These and related questions are then applied to a new class of convex bodies which is a natural generalization of the class of zonoids: the class of belt bodies. Finally open research problems are discussed.

Excursions into Combinatorial Geometry

We survey mainly recent results on the two most important orthogonality types in normed linear spaces, namely on Birkhoff orthogonality and on isosceles (or James) orthogonality. We lay special emphasis on their fundamental properties, on their differences and connections, and on geometric results and problems inspired by the respective theoretical framework. At the beginning we also present other interesting types of orthogonality. This survey can also be taken as an update of existing related representations.

On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces

I. Nonclassical Variational Calculus. II. Median Problems in Location Science. III. Minimum Convex Partitions of Polygonal Domains.

Geometric Methods and Optimization Problems

This is a review of various problems and results on the illumination of convex bodies in the spirit of combinatorial geometry. The topics under review are: history of the Gohberg-Markus-Hadwiger problem on the minimum number of exterior sources illuminating a convex body, including the discussion of its equivalent forms like the minimum number of homothetic copies covering the body; generalization of this problem for the case of unbounded convex bodies; visibility and inner illumination of convex bodies; primitive illuminating systems for convex bodies; illumination and visibility of families of convex bodies; clouds formed by translates or homothetic copies of a convex body; miscellaneous results.

Horst Martini

Papers

Excursions into Combinatorial Geometry

On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces

Geometric Methods and Optimization Problems

Combinatorial problems on the illumination of convex bodies

Bodies of Constant Width: An Introduction to Convex Geometry with Applications