Affinely associated bodies

01.06.2003 - 31.03.2007
Research funding project
Some of most fundamental objects in mathematics are functions and bodies in ordinary Euclidean space. These are used to represent real objects and phenomena in science and engineering. Here we are interested in properties of these objects that are invariant under linear or affine transformations. Although an affine structure contains no notion of distance or angle, there is still a rich and deep theory that already encompasses many of the most important aspects of Euclidean geometry. The goal of the project is to give a classification of those bodies and functions that are linearly or affinely invariant and have simple additivity properties. This should lead to a better understanding of affine geometry and could prove to be useful in fields ranging from pure mathematical areas such as differential geometry and functional analysis to more applied areas such as information theory and stereology.

People

Project leader

Project personnel

Institute

Grant funds

  • FWF - Österr. Wissenschaftsfonds (National) Austrian Science Fund (FWF)

Research focus

  • Beyond TUW-research focus: 100%

Keywords

GermanEnglish
konvexe Körperconvex bodies
BewertungenValuations
affininvariantaffinely invariant

Publications